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Monitoring mechanical vibrations using a histogram recorder
Monitoring mechanical vibrations using a histogram recorder J. R . S c h n i t t g e r
The problem of fatigue failures originating from random vibrations in machine tools and process machinery calls for new methods of monitoring these machines before demands of higher productivity and increased performance can be met. A laboratory model of a simple r o t o r system has been built to study different ways in which 'normal' and 'abnormal' cond/t/ons of random vibrations m a y be established. A Datamyte histogram recorder was used to collect, digitize and store the results from the r o t o r when subject to different degrees of imbalance. It was found that the real-time rainflow and time-at-level and level crossing programs could be used to indicate abnormal vibrations arising from a 0.1% change in r o t o r mass imbalance.
Key words: fatigue; vibration testing; rotors (mechanical); mathematical analysis
For at least two decades, different methods have been employed to survey the operation of large machine systems like turbines, paper mills, naval propulsion machinery, steel mills and high-precision machine tools. One standard method has been t o use accelerometers for automatic alarm or trip-out at a preset limit. More sophisticated devices record the most recent analogue signals which may be permanently saved in the case of an alarm. Impulse shock wave mea=urement using the SPM method has given excellent precisionin the vicinityof balland rollerbearings.
The rotor The model (Fig. 2) was fabricated using plexiglass for the frame and a c o m m o n steel for the shaft ( 5 m m thick) and the rotor (1 kg in weight; diameter 9 0 m m ; thickness 20 mm). The rotor system was supported by two ball bearings, 200 m m apart, one of which had a flexible bearing support. The rotor had three critical speeds; one at about 2000 rev/ rain with a second multiple at 4000 rev/min relating to the
Conditions of hydrodynamic bearingsm a y be monitored by temperature measurements, even if thismethod ismore apt to detect changes in oil flow distribution. However, the study of vibrationremains an important means of following both the actual condition of machinery and possibly changing dynamic loads on the system. Harmonic analysisof the analogue signalsto establishthe natural modes of vibrationis particularlyimportant, but it does not lead directlyto a measure of 'normalcy',nor does ityield any information about 'time average' or possible 'cumulative'damage to the machinery in any given time. This paper examines the usefulness of a new class of digital devices, the histogram recorders, in monitoring mechanical vibrations.
Fig. 1 The Datamyte 400 histogram recorder
The histogram recorder The Datamyte 400, manufactured by Electro General Corp, Minnetonka, MN, USA, was used in this study. It is a small, robust microprocessor, 200 x 200 × 100 mm in size, and is shown in Fig. 1. It may at present be provided with any one of seven different programs in small hardware packages. This single-channel instrument converts analogue signals below 200 Hz into digital information and stores the processed information in a RAM m e m o r y box, which has a capacitor to maintain voltage if external power is lost. Due to the elimination of time as a variable, the histogram recorder can retain information on behaviour over longer
time periods. The standard RS232C serial port interface makes it possible to extract the actual accumulated time averages as often as desired. Either the accumulation process may continue after an interruption or a new time averaging process may be initiated.
Fig. 2 The model rotor system showing the drive system to the left and the displacement and speed sensors to the right
0 1 4 2 - 1 1 2 3 / 8 3 / 0 3 0 1 4 5 - 0 9 $3.00 © 1983 8 u t t e r w o r t h & Co (Publishers) Ltd
Int J Fatigue Vol 5 No 3 July 1983
145
rotor mass rotating on the shaft, and a third relating to the low speed vibration of the bearing support. The original rotor had an imbalance of approximately 1.5 g at the rotor periphery, corresponding to 0.15% of the rotor weight. Placing a small weight of 1.5 g in either of two peripheral holes, it was possible to obtain three configurations of imbalance named B0, B1 and B2 respectively with zero, 0.15% and 0.30% imbalance. A steel weight on the plexiglass stabilized the model and served as a fixture for the dual spring of the right hand bearing (see Fig. 3). Closer to the shaft, a 3 0 m m long phosphor-bronze spring with four active strain gauges was used to measure the lateral deflection of the plexiglass support in the vibratory mode (120 ohm gauges, gauge factor 2.05). The model was also equipped with two small Ferroxdure disc magnets glued to the end of the shaft, which activated a Hall-effect switch (of the Archer type, by Radio Shack). The semiconductor switch acted on a Clare reed relay 1A05 from General Instruments. This small system provided two short circuits per shaft revolution at the No 1 switch of the Datamyte input. The rotor was brought up to the desired angular speed by a small 12V high-speed miniature drill. A small friction drive wheel was pressed manually against the smooth wheel surface at the left end of the rotor.
Experimental procedure All test runs were performed following the same general procedure. For each run the Datamyte computer was first initiated from a Teletype 43 printer keyboard. The actual recording, however, was delayed until the rotor reached 4000 rev/min as checked by a stroboscope directed onto
the shaft. When this speed was reached, the small driving drill m o t o r was entirely removed from the model and the starting signal for recording (a carriage return from the keyboard) was given. In this way, the Datamyte recorded the rotor behaviour from 4000 rev/min down to a complete stop. Each configuration of imbalance was tested repeatedly using four of the available Datamyte programs. The realtime rainflow counted the number of rainflow ranges, with due regard to their magnitudes. The time-at-level and level crossing totalled the amount of time an analogue signal was present in each 'level' and counted each time a level was crossed. The sequential peak and valley program recorded extreme values of the random analogue signal. Finally, the XY-intercept was employed to record the deflections of the rotor bearing as a function of the rev/min. The signal conditioner module of Datamyte 400 has a gain adjustable by discrete steps. The output of this unit represents the input to the true computer section of the Datamyte system. There are 64 'levels' between + 5 V and --5 V as defined at the computer input (see Fig. 4). However, only the voltage range of .+2.5 V was actually processed according to the programs mentioned above. This range was divided into 32 levels at the computer output, corresponding to -+3% resolution in the digital representation of the analogue signal. Nevertheless, the events on the levels 0 to 15 and 48 to 63 at the computer input were not entirely discarded. The number of valleys and peaks in these levels were counted and those counts were part of the Datamyte output to the printer. The present series of experiments were all made with a gain factor of 7500 across the signal conditioner. The model system and the conditioner were calibrated so that a deflection of the spring-mounted bearing support of •+0.85 mm corresponded to the full measuring range, that is to levels 0 and 31 at the computer output. The Datamyte has two kinds of filters: the signal conditioner contains an analogue low pass filter which is factory set at approximately 250 Hz at -- 3 dB; there is also a 'digital filter' referred to as an 'adjustable hysteresis'. For example, if the hysteresis input is set at HYS 5 with the rainflow program, all range counts of magnitude of ~"'~. levels or less are suppressed and do n o t appear at the computer output. As a separate complement to the Datamyte recordings, the amplified analogue signal available at the output of the signal conditioner was studied with a Brush pen recorder.
ResuIts Rain flow recordings
Fig. 3 A close up of the r o t o r showing the t w o sensor systems
146
The real-time rainflow algorithm has already been described elsewhere. 1 One rainflow range count is demonstrated in Fig. 4, where it stretches over ten levels, ie 10/32 parts of the 'full scale output'. Eighteen rainflow runs were undertaken according to the procedure just described. The output signal was observed with a digital voltmeter at the complete stop after each run. One of the eighteen recordings was discarded because its final static reading was considered to deviate too much from the initial setting before the run, ie by some 10% of the full output scale defined in Fig. 4. The scheme used to give some degree of statistical confidence in the results was as follows. For every one of
Int J Fatigue July 1983
+2 x Full scale
To computer
From computer
Input bond definition
Output bond definition
65
8 +2.5V
+ Full scale
Tension direction Signal conditioner
!=
,Gain7 5 0 0 ~ ' J
-
+Full scale
t Zero
Compression direction
+5V
51 52
I
0V
16
i
- 7,~,,~T Rainflow range
I
-Full scale
16 15 -2.5V
(3
- -Full scale
DC volts at output of signal conditioner
-2 x Full scale
0
-5V
Fig. 4. Definitions of signal gain, computer input and output levels (bands), showing one rainflow range count of magnitude 10 levels
the three configurations B0, B1 and B2 four consecutive runs were recorded. These were intended to establish a possible 'normalcy' at each level of rotor imbalance (0, 0.15% and 0.30%). The behaviour of the B1 rotor was studied by purring the output of the Datamyte signal conditioner module into the input terminals of a Brush Mark 280 pen recorder. The Datamyte was set at maximum gain and the recorder adjusted to a sensitivity of 2 mV/line and a paper speed of 50 mm/s. The results are shown in Fig. 5. Fig. 5a shows the onset of double critical shaft speed vibration at 3800 rev/min. The beginning of shaft critical speed vibration at 2000 rev/min is shown in Fig. 5b. Fig. 5c shows the passage through the low speed bearing support vibration at 500 rev/min, the maximum amplitude of which corresponds to about -+1 mm displacement amplitude of the bearing support. The recording of the balanced configuration, B0, and that of the most unbalanced, B2, may be compared. For both, the hysteresis setting HYS 5 suppressed all range counts below or equal to five levels of magnitude (see Figs 6 and 7). These recordings reveal obvious differences in behaviour. Firstly, it can be noted that the total number of range counts for the balanced rotor is 334 and for the unbalanced no less than 1889. Secondly, there are far more range counts of large magnitude for the unbalanced rotor. The balanced rotor had only 20 counts whereas the unbalanced one had 249 counts. Thirdly, besides the range counts, the Datamyte records the peaks and valleys in the input side bands 4 8 - 6 3 and 0 - 1 5 respectively. The balanced rotor had none, the unbalanced 34 peaks and 49 valleys in those bands. This means that the flexible bearing support was deflected more than 0.85 mm out of the static no-run position. R a i n f l o w damage i n d e x
Socie 1 has discussed life estimation techniques from rain-
Int J Fatigue July 1983
flow counted histograms and has distinguished between load or stress life analysis and strain life analysis. The fatigue life is based on the sum of the fatigue damage, Di, experienced for each load range, where D i = N/Nf. Here N is the number of rainflow range counts and Nf is the number of cycles to fatigue failure at any given constant amplitude. In this concept of linear cumulative damage, the total damage D is:
D : ~ D i = ~. (N/Nf) i i
i
It is also considered that D = 1 corresponds t o the most
probable fatigue life. This assumption has been frequently criticized although nothing better has been proposed in connection with the present techniques of measuring fatigue in mechanical engineering. The load-life approach applies to cases where the actual component is being tested rather than a laboratory specimen. An equation of the following form has been shown to fit fatigue data: A p -- p'(2Nf)m where Ap = load range = constant x R; R = rainflow range; and m =--0.2223. The present project is motivated by the hypothesis that a fatigue life monitoring scheme should be based on the cumulative damage theory. However it was not considered necessary at this stage to scale the rainflow damage index so that D = 1 would be a precise final alarm. In other words, the linear scale factor could be more arbitrarily assigned. From the above relationship (Ap =f(Nf)), it may be written: 1 R = --" (Nf) -0'2223 k
or
Nf = (kR) -4"50
147
g. 5 The behaviour of the 61 rotor system: (a) double critical shaft speed vibration revlmin (c) low speed bearing support vibration at 500 revlmin
at 3800
rev/min
(b) shaft critical speed vibration
at
2(,bO
Assuming a series of constant amplitude experiments, so that DI = and assigning value 1 D for = 31 Nf = the following be obtained: = (0.006949 This value would give results calculated Table 1. physical motion the bearing would be x 0.85 1.70 mm the rainflow count of This may compared with Bl configuration with the pen recorder. maximum low vibration amplitude to a count of tude 2 Table 1 demonstrates the of large ranges in damage index. above formulae applied to Datamyte recordings. each individual set of and rainflow counts, a value was by the of the = f(R) The D ZDi values plotted in 8.
148
D
from 0.032
0.0665 based
four runs
each
rotor A second of five (BO, Bl, 82, B2) an almost relationship between and the imbalance. In the relatively D value the balanced was not in this round of Table 1.
values of
damage index Rainflow damage D
Rainflow counts,
Nf 1 000 7189
1000 1000
1 00 0.13900 15
10
Int
Fatigue
July
DATAMYTE 451-23
-
RI--AL--rIMER(IIN FLOW T:IME: 0,1 d:[R X 01
rEST N A M E ~ 4YS= 5
IDI2D=I
SHUTDN OFLOW 0
T:[ME SWO
29
0
>+FS 0
0
SWI
SW2
0
0
<-FS +2*FS -2*FS +PEAK -F'EAK 0 O 0
RANGE COUNT FULL CYCLES .
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the extreme levels 1, 2, 3, 29, 30 and 31 were counted for a number of runs as shown in Table 2. Even though it may be argued that the counts of level crossings should be made over an equal time period, it could be counter-argued that the runs all covered the same passage through three critical speeds. i)AT,~HY[E .~51-23
HIS= 5
i~!Ii~ x :)i
IDx2D=I
SHUTDN OFLOW TIME 0
.
.
00000000
Fig. 6 Rainflow data for BO rotor
0
(~
<-FS +2*FS -=.~F,.~ +F'F-'AI(-PEAl< 17 62 I 49 2
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18 00000109 17 00000024
Provided that a larger number of samples for the 'normal' condition of real, full scale machines are used, the damage index D could be a trustworthy single parameter index to m o n i t o r deterioration of the dynamic behaviour. Balanced rotors would always give a rather low index, whereas an increase in the index after a certain time of operation would indicate worse conditions and the onset of fatigue and wear.
I;:.~ 00000039 19 00000005
20 OOO00005 21 00000004 22 00000004 23 OO00000J
24 O00000oi 25 00000004 22 ou,:)O0002
Time-at-level and level crossing recordings
The number of crossings (over more than nine levels) to
..%
0
6 000002,59 7 00000328 i~ 00000104 9 00000168 10 00000124 I I 00000171 12 00000107 1:3 00000118 14 00000058 15 00()00198
00000001
Level crossing index, LCI
0
27
RANGE COUNT FULL CYCLES .
00000001 00000010
The time-at-level and level crossing program totals the amount of time an analogue signal is present in each of the 32 levels of the computer output, as presented in Fig. 4. The program also counts each time one of the 32 levels is crossed (entered) and it stores the counts for each level. Thirteen runs were recorded for the three rotor configurations to examine if level crossing counts could perhaps be used for a single parameter index similar to the rainflow damage index. All o f the level crossing recordings were made at maximum suppression of the smaller scale level crossings, so that no level crossings equal to or less than nine levels between a peak to the next valley or vice versa were recorded; this appeared to be the best f o r m a t for the indication of abnormal conditions. The balanced B0 rotor and the unbalanced B2 were recorded as shown in Figs 9 and 10. Fig. 9 shows that the flexible bearing deflection was very moderate and close to zero, since it stayed on levels 13, 14 and 15 for 87°,/0 of the time. The unbalanced rotor spent 60% o f its time in close-to-zero conditions. Furthermore, level crossings over more than nine levels to or from levels 1, 2 and 3 or 29, 30 and 31 respectively were considerably more numerous for the unbalanced rotor.
0
?+FS 34
12 00000008
Int J Fatigue J u l y 1983
(I[ME.: 0.1
iES~ ~ A M E ~
.
6 00000167 7 00000087 8 00000028 9 00000007 10 00000002 11 00000006 12 00000002 13 00000005 14 O0000001 15 00000009 113 19 20 31
rq:iAl_-TlJ~iE R~.IN Fi O!,J
-
2!.-,' 00000004
2q 00000004 30 00000004
L(I 00000037 4: Fig. 7 Rainflow data for B2 rotor
? 0
c3
6 5
o
E
o
4
o•
2
I o
9
O
I
i
I
2
i
3
Irnbolonce (%) Fig. 8 R a i n f l o w damage i n d e x , D as a f u n c t i o n o f relative r o t o r i m b a l a n c e : o average values o f f o u r tests f o r each r o t o r i m b a l a n c e , o sample tests a f t e r establishing t h e average values
149
Table 2. Variation of level crossing counts with rotor imbalance
Rotor
BO
81
B2
Number of level crossings (over levels 1 , 2 , 3, 29, 30, 31 )
Time duration of run (min)
Average counts o f level crossings
3.2 3.4
13
297 321
3.3 3.2
314
1331 415 171 343
2.2 2.4 2.7 2.5
565
HYS:9 TEST NAME [002 TEST BEGUN
-
T;[ME-AT-LEVEL + LEVEL CROSSING
TEST NAME TO02
TIME: 0.1 M~N X 01
HYS= 9 SHUTDN OFLOU TIME SWO 0 0 32 0
SWI 0
BIN COUNTS COUNTS% NO. AT 800 0 000000000024 000.01% I 000000000013 000,00% 2 000000000105 000.06% 3 000000000143 000.09% 4 000000000157 000,I0% 5 000000000185 000.11% 6 000000000225 000.14% 7 000000000249 000.15% 8 000000000365 000.23% 9 000000000530 000.34% 10 000000000791 000.50% 11 000000001837 001.17% 12 000000007726 004,96% 13 000000032968 021.16% 14 000000077529 049.78% 15 000000024984 016.04% 16 000000003581 002.29% 12 000000001645 001.05% 18 000000000852 000.54% 19 000000000432 000.27% 20 000000000380 000.24% 21 000000000276 000.17% 22 000000000192 000.12% 23 000000000149 000.09% 24 000000000157 000.10% 25 000000000128 000.08% 26 000000000096 000.06% 27 000000000002 000.00% 28 000000000002 000.00% 29 000000000004 000.00% 30 000000000004 000.00% 31 000000000011 000,00% TOTAL COUNTS 000000155742
SW2 0 LEVEl_ CROSSING 0000000~ 00000003 00000014 00000030 00000042 00000054 00000068 00000083 00000102 00000123 00000131 00000131 00000131 0000013I 00000131 00000131 00000131 00000132 00000132 00000122 00000101 00000078 00000060 00000049 00000039 00000029 00000013 00000002 00000002 00000002 00000002 00000001
Fig. 9 Time-at-level and level crossing data for BO rotor
150
:~:F'
DATAMYTE 454-11
TIME-AT-LI-VEL ÷ LEVI-L CI~OS!~INI
FEST NAME TOIl
23 2
*F' DATAMYTE 454-11
H¥S= 9 [EST NAME T011 fEST BEGUN
rIME: O.l
M:[N X Ol
IIYS= 9 SHUTDN OFLOW TIME 0 0 24
S~O 0
SW1 0
SW2 0
BIN COUNTS COUNTS% NO. AT 800 0 000000000683 000.61% I 000000000161 000.14Z 2 000000000223 000.19% 3 000000000314 000.28% 4 000000000575 000.51% 5 000000000955 000.85% 6 000000001246 001.11% ? 000000002070 001.84% 8 000000002996 002.67% ? 000000003537 003.18% 10 000000004685 004.18% 11 000000004362 003.89% 12 000000005673 005.06% 13 000000007467 006.67% 14 000000016592 014.82% 15 000000034346 030.68% 16 000000008387 007.49% 17 000000006285 005.61% 18 000000004245 004.23% 19 000000002351 002.10% 20 000000001643 001,46% 21 000000000935 000.83% 22 000000000537 000.47% 23 000000000327 000.29% 24 000000000181 000.16% 25 000000000071 000.06% 26 000000000063 000.05% 27 000000000040 000.03% 28 000000000045 000.04% 29 000000000039 000.03% 30 000000000042 O00,03X 31 000000000339 000.30% TOTAL COUNTS 000000"111915
LEVEl_ CROSSI[NG
00000036 00000113 00000189 00000269 00000416 00000653 00000902 00001182 00001522 00001720 00001875 00002'125 00002291 00002322 00002322 00002322 00002316 00002274 00002051 00001202 00001347 00000942 00000573 00000294 00000126 0000005? 00000041 00000037 00000035 00000033 00000030 00000014
Fig. 10 Time-at-level and level crossing data for B2 rotor
Therefore the average of counts obtained for the three configurations was seen as a relevant index. To obtain an index similar to the rainflow damage index, the following was used: LCI -- (average count)/10 000 Fig. 11 shows that there is an almost linear relationship between LCI and the percentage imbalance. The wellbalanced rotor exhibits an extremely low LCI. Also, even a slight imbalance consistently raises the LCI significantly.
Sequential peak and valley recordings The sequential peak and valley program provided a very distinct and different record for the tested rotors with respect to their degree of imbalance. This program is the only one in the study which has a partial flavour of the time variable, since it records the extreme high and low
Int J Fatigue July 1983
5
~o
6
4
0
I
0
I
I
2 Imbolonce (%)
1 3
Fig. 11 Level crossing index, LCI, as a function of relative rotor imbalance. LCI is counted for bands 1,2, 3, 29, 30 and 31 DATAMYTE 452-04
SEQUENTIALPEAK-VALLEY
TEST NAME SS003
BEG. HYS=09 ISHUTDN OFLO~ 0
>+FS 0
0
TIHE: 0.1MIN X Ol END HYS=09
TIME
S~O
Sgl
0
0
29
5~2 0
K-FS +2*FS -2*FS +PEA~C-PEA~( 0
0
this program with 16 deflection columns. The rev/min pulses (2 per rev) are resolved into a maximum of 32 bands for 300 Hz. Running the rotor at 4000 rev/min thus corresponds to 4000(2/60) (32/300) = 14 bands or rows in the Datamyte print. Most of the readings are concentrated in columns 7 and 8 which correspond to small or zero deflection. Also, each count in Fig. 15 represents the average value over 0.427 seconds. The extreme deflections, as already recorded by the previous programs, do not usually last that long. Therefore the XY-intercept is most useful in monitoring slightly more permanent characteristics. The different passage phases may easily be detected in Fig. 15. The supercritical speed counts are concentrated in column 8. The critical shaft speed (around 1500 rev/min) moves the counts into columns 6 and 7, whereas the rows 5, 6 and 7 correspond to a speed range between 1400 and 1970 rev/min. In row 1, ie 280 rev/min and below, a count in column 5 occurs, which represents the passage into the low speed large deflection phase. A double number of pulses for each revolution would have improved the present rev/min resolution with this program. However it has been sufficiently demonstrated that the program provides a frequency response, though averaged, both with respect to each cycle and to the longer time average.
0
PEAK AND VALLEY DATA
20,I0,20,09,20,09,20,09,20,09,20,09,20,09,20,0!3,20,08,20,08 20,08,21,08,21,07,21,07,21,07,21,07,22,07,22,06,22,06,22,06
DATAMYTE 4 5 2 - 0 4
23,06,23,06,23,05,23,05,23,05,24,05,24,05,24,05,24,05,24,04
TEST NAME S002
24,04,24,04,25,04,25,04,25,04,25,04,25,04,25,03,25,03,25,03 25,03,26,03,26,03,26,OJ,26,03,Z6,04,25,04,25,v4,25,05~25,05 24,05,24,06,23,07,22,08,21,08,21,09,20,10,20,~0,20,10,20,10 20,09,20,I0,20,09,20,10,21,09,20,09~21,09,20,09,2~,09,20,'I0 21,09,20,10,21,10 Fig. 12 Sequential peak and valley data for BO rotor. The test was run w i t h m a x i m u m i n i t i a l
hysteresis
BEG, HYS=O9
SEQUENTIALPEAK±VALLEY TIME: 0.I RIM X 01
END HYS:I3
SHUTDN OFLOg TIME SgO 0 0 26 0
Sgl 0
Sg2 0
>+FS <-FS +2*FS -2*FS +PEAl.( -PEAH I? 30 3 ? 62 1 PEAK ANO VALLEY OATA
values of the deflection transducer sequentially. This facilitates the study of the actual dynamic behaviour of the rotor system. The balanced B0 rotor is represented in Fig. 12. Since the initial 'hysteresis' is set at the maximum value of nine bands, all the smaller deflections are left unrecorded. This could be helpful in the case of monitoring, whereas a study of fracture mechanics would be conducted with zero hysteresis. The behaviour of the B2 rotor is described in Fig. 13 and graphically in Fig. 14. Despite the suppression of the smaller deflections the run exhausted the entire m e m o r y space of the Datamyte. On the left of Fig. 14, well above the critical speed, the rotor shows relative stability. The next two sequences correspond to the onset of larger amplitudes when passing through the shaft critical speed at about 1500 rev/min. At the right end of Fig. 14, it becomes clear that passage through the very low speed deflection of the support springs creates the most severe load on the system. This effect was not distinguished by the other programs.
10,24,10,24,10,24,10,24.09,24,09,24,09,24,09,24,09,25,0%25
09,24,09,25,09,25,08,25,08,25,09~25,08,25,08,25,08,25,08,25 oe,26,o8,26,o8,26,o8,26,o8,26,o8,26,08,26,08~26,08,26,08,28 08,27,08,26,08,26,08,26,08,26,08,27,08,27,08,27,08,27.08,27 08~27,08.27,08,27,08,27~08,27,08~27,08,27~08,27,08~27~08,27 08,27,08,27,08,27,08,27,08,27,08,27,08,27,08,27,09,27,09,27 09,27,09,27,09,27,09,27,08,27,09,27~09,27,09,27,09,27,09,26 09,26,09,27,09,27,10,27,10,27,09,26,09,26,09,26,09,27,I0,27 10,27,10,26,09,26,09,26,09,26,09,26,10,27,10.27,10,27,10.26 "10,26,~0,26,10,26,t0,26,10,26,10,26,~0,26,10,26,10,26.10,26 II,26,11,26,11,26,1I,26,II,26 II,26,11,26,11,26,1"I,26,Ii,26 I 1,26, 11,2,:~,I1,26,11,26,11,26,11,26 i 26,II,26,II ,~6,12,26, ~ -1 ,i ,~ 9 ~ 9 9' 1 2 , 2 6 ,~6,1~,~6,I I ,26,I 1,26,11.26,
10,.6,11 ,.6,11,26,11,26,11,26, ,26,11,26,11,26,11,26,11,26,
2,26,12,26,1~,.6~° .~ 12,26,12,26, . : ~6,1 . , , ~ 6 , I ~ ~.~8, 1 2 , 2 6 , 1 2 , 2 6 ,
12,26,12,26,12,28~12,28,19
?~i
12,26,12,2~,12,2~,~2,26,1::2;I
2,26,12,26,12,26,12,26,12,26, 06,20,06.20~06,20,08,20,06,20 06,20,06,20,06,20,06,20,06,20, 0a,~0,0~,.0,05,.0,06,~0,05,-0i 06,20,05,20,06,20,05,20,06,20, o~,~o,o~;~o;o5;~,o5,~,o5,~o 05,1q,05,20,06,20,05,20,05,20,06,20,05,19,05,20,05,20,05,20 05~20~05,19,05,19,05,19,05,17,05,19,05,1%05~19~05,17,05~19' 05,19~05j19~O5,19,05~lg~OS,19,05~lgy05,1%05~20,05~21~07,21
07,21,07,21~07,21~07,21,07,21,07~21,01,22,07,22,07,22,07,22 07,22,07,22,07,22,06,22,06,22,06,23,06,22,06,22,05~23,05,23 05,23,05,23,05,23,05,23,05,23,05,23,05,23,05,24,04,24,04,24 04,24,04,24,04,24,04,24,03,24,03,24,03,25,03,25,02,25,02,25
Time a t X Y-intercept recordings
02~25,02,25,02,25,02,26,01,26,01,26,01,27,00,22,00,22,00,22
In this program, the load variable (deflection) is limited to 16 bands for the full scale deflection, so all the values for deflection should be doubled for comparison with those of the other programs. Fig. 15 for a B2 rotor demonstrates the format of
00,31,00,31,00,31,00,31,00,31,00,31,00,31~00~31~00,31~00,31
Int J Fatigue July 1983
00,28,00,28,00,28,00,28,00,29,00,29,00,2%00~30,00,30,00,31 00,31,00,31,00,31,00,31,00,31,00,31,00,31,00,31,00,3'1,00,~1
00,31,02,28,04,26,06,25,07,25,07,25,07,25,07,25,07,25,07,24 08,24,08,24,08,24,09,23,09,23,09,23,09~23,09 Fig. 13 Sequential peak and valley data for B2 rotor. The test was run with maximum initial hysteresis
151
L
I:=, soo2
3°I
1 82• ,
I ,
I
=
e c- 2 0
8 ==
....
-o
L--C_
g io
dSUperc 0 F i g . 1 4 D i s p l a y o f digital data from sequential peak and valley program. The time variable has been simplified to give equal distance between the peaks over the whole region
DATAMYTE
E1ME-AT-XY- IN'[ERSEC[S
455-06
TIrME: 0.1 MIN X 01
lEST N A M E ~ 9HUTDN 0 ROg NO.
OFLOW
TIME 0
COLUNNS 0
25
ROTOR
SPEED
DEFLECTION
I
2
3
4
5
12 13 51
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0,1500 0 0 0 0 0 0 0 0 4000 O"
0 0 0 0 0 rpm 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
lOT
O0
O0
O0
01
00 01 02 03 04 05 06 O7 08 O? I0
II
O0
O0
?
8
9
0 0 ? 0 0 13 I? 1S 0 0 0 0 0 0 0
0 119 I ,54 2? 0 35 0 27 0 I 0 0 0 I 0 l0 0 4 5 0 9 0 6 0 8 0 4 0 0
0 0 0 0 0 0 0 0 0 0 ~ 0 0 0 0
49
106 205
O0
11
12
0 0 ,3 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
O0
O0
0,.
I0
13 0 0 0 0 ,) 0 0 0 0 0 0 ,:) 0 0 0 O0
14 0 0 0 0 ,) 0 0 0 0 0 0 0 0 0 0 .)0
115 0 0 0 0 ', 0 0 0 0 0 ,i ,3 0 0 0 Ov
TO IAI. i I':~ !~6 31 3'~ 2? ]4 I: I3 10 ,~ ,37 9,:~ 0 04 ,:~:, 3~]
F i g . 15 T i m e at the X Y intercept for B 2 r o t o r
Design of a monitoring system
•
Once the feasibility of a single parameter index for a given machine system has been established, the actual design of a complete monitoring instrument may be considered. In particular, the following points should be considered:
•
•
Is it desirable to have more than one sensor and therefore to arrange for scanning with a multiplexer that connects the Datamyte to two or several sensors in a sequence?*
* I t has been suggested that one ought to use a multichannel device. A t the time of this research project, no such devices were on the market at a reasonable price. Even if several systems are arranged in one frame, they still constitute that many separate microcomputers.
152
• •
•
To what extent would it be desirable to save more permanently the recordings taken during any time interval? How long should each transducer be connected to the Datamyte: 10 000 or 1000 seconds? What exact form of the index is most suitable? Should the collection of the originalvalues of 'normal' conditions be an integrated, automated sequence of monitoring equipment? What hardware configuration would be best for more permanent memory storage?
When the answers to the above questions are better known, the monitoring system can be designed. The objectives of the design would preferably be an effective low cost
Int J Fatigue July 1983
Parallel interface
I
Transducer
I
ALU
~=~
RAM
zE~Operotionoi E ~ amplifiers i
r=L interface
i
Address bus
Fig. 16 Possible design of Dynalog system for condition monitoring of machine systems. The address bus communicates signals to the transducer multiplexer to switch the desired transducer channel to the histogram recorder and looks up the permanent memory for individual fingerprints. The executive communicates with the histogram recorder (both addressing and data transfer) via a standard EIA 232 serial interface
alternative, in line with the general philosophy of modem self-sustained histogram recorders. One example of the layout for the monitoring equipment is illustrated in Fig. 15.
Conclusions Using an inexpensive laboratory model a preliminary
Int J Fatigue July 1983
investigation into the use of histogram recorders for monitoring mechanical vibrations has been made. The results should only be considered as indicative and are intended to serve as guidelines for the design of real life equipment. All tests were duplicated several times for observation of consistency in the data and in the return to static readings after each complete stop. However, the number of tests for each case was not large enough to establish statistical parameters with any acceptable degree of confidence. On the other hand this was not necessary in order to verify the basic hypothesis that both real-time rainflow and the level crossing programs should provide a basis for a single index to detect early tendencies of deterioration in dynamical behaviour. The peak and valley and the XY intercept programs supported the data of the first two programs and provided useful, complementary information about the model.
References Socie, D. F. 'Fatigue life estimation techniques' Technical Report No 145 (Electro General Corp, 1981)
Author Professor Schnittger is with The Royal Institute of Technology (KTH), Department of Machine Elements, Brinellv~gen 68, S-10044 Stockholm, Sweden.
153
The problem of fatigue failures originating from random vibrations in machine tools and process machinery calls for new methods of monitoring these machines before demands of higher productivity and increased performance can be met. A laboratory model of a simple r o t o r system has been built to study different ways in which 'normal' and 'abnormal' cond/t/ons of random vibrations m a y be established. A Datamyte histogram recorder was used to collect, digitize and store the results from the r o t o r when subject to different degrees of imbalance. It was found that the real-time rainflow and time-at-level and level crossing programs could be used to indicate abnormal vibrations arising from a 0.1% change in r o t o r mass imbalance.
Key words: fatigue; vibration testing; rotors (mechanical); mathematical analysis
For at least two decades, different methods have been employed to survey the operation of large machine systems like turbines, paper mills, naval propulsion machinery, steel mills and high-precision machine tools. One standard method has been t o use accelerometers for automatic alarm or trip-out at a preset limit. More sophisticated devices record the most recent analogue signals which may be permanently saved in the case of an alarm. Impulse shock wave mea=urement using the SPM method has given excellent precisionin the vicinityof balland rollerbearings.
The rotor The model (Fig. 2) was fabricated using plexiglass for the frame and a c o m m o n steel for the shaft ( 5 m m thick) and the rotor (1 kg in weight; diameter 9 0 m m ; thickness 20 mm). The rotor system was supported by two ball bearings, 200 m m apart, one of which had a flexible bearing support. The rotor had three critical speeds; one at about 2000 rev/ rain with a second multiple at 4000 rev/min relating to the
Conditions of hydrodynamic bearingsm a y be monitored by temperature measurements, even if thismethod ismore apt to detect changes in oil flow distribution. However, the study of vibrationremains an important means of following both the actual condition of machinery and possibly changing dynamic loads on the system. Harmonic analysisof the analogue signalsto establishthe natural modes of vibrationis particularlyimportant, but it does not lead directlyto a measure of 'normalcy',nor does ityield any information about 'time average' or possible 'cumulative'damage to the machinery in any given time. This paper examines the usefulness of a new class of digital devices, the histogram recorders, in monitoring mechanical vibrations.
Fig. 1 The Datamyte 400 histogram recorder
The histogram recorder The Datamyte 400, manufactured by Electro General Corp, Minnetonka, MN, USA, was used in this study. It is a small, robust microprocessor, 200 x 200 × 100 mm in size, and is shown in Fig. 1. It may at present be provided with any one of seven different programs in small hardware packages. This single-channel instrument converts analogue signals below 200 Hz into digital information and stores the processed information in a RAM m e m o r y box, which has a capacitor to maintain voltage if external power is lost. Due to the elimination of time as a variable, the histogram recorder can retain information on behaviour over longer
time periods. The standard RS232C serial port interface makes it possible to extract the actual accumulated time averages as often as desired. Either the accumulation process may continue after an interruption or a new time averaging process may be initiated.
Fig. 2 The model rotor system showing the drive system to the left and the displacement and speed sensors to the right
0 1 4 2 - 1 1 2 3 / 8 3 / 0 3 0 1 4 5 - 0 9 $3.00 © 1983 8 u t t e r w o r t h & Co (Publishers) Ltd
Int J Fatigue Vol 5 No 3 July 1983
145
rotor mass rotating on the shaft, and a third relating to the low speed vibration of the bearing support. The original rotor had an imbalance of approximately 1.5 g at the rotor periphery, corresponding to 0.15% of the rotor weight. Placing a small weight of 1.5 g in either of two peripheral holes, it was possible to obtain three configurations of imbalance named B0, B1 and B2 respectively with zero, 0.15% and 0.30% imbalance. A steel weight on the plexiglass stabilized the model and served as a fixture for the dual spring of the right hand bearing (see Fig. 3). Closer to the shaft, a 3 0 m m long phosphor-bronze spring with four active strain gauges was used to measure the lateral deflection of the plexiglass support in the vibratory mode (120 ohm gauges, gauge factor 2.05). The model was also equipped with two small Ferroxdure disc magnets glued to the end of the shaft, which activated a Hall-effect switch (of the Archer type, by Radio Shack). The semiconductor switch acted on a Clare reed relay 1A05 from General Instruments. This small system provided two short circuits per shaft revolution at the No 1 switch of the Datamyte input. The rotor was brought up to the desired angular speed by a small 12V high-speed miniature drill. A small friction drive wheel was pressed manually against the smooth wheel surface at the left end of the rotor.
Experimental procedure All test runs were performed following the same general procedure. For each run the Datamyte computer was first initiated from a Teletype 43 printer keyboard. The actual recording, however, was delayed until the rotor reached 4000 rev/min as checked by a stroboscope directed onto
the shaft. When this speed was reached, the small driving drill m o t o r was entirely removed from the model and the starting signal for recording (a carriage return from the keyboard) was given. In this way, the Datamyte recorded the rotor behaviour from 4000 rev/min down to a complete stop. Each configuration of imbalance was tested repeatedly using four of the available Datamyte programs. The realtime rainflow counted the number of rainflow ranges, with due regard to their magnitudes. The time-at-level and level crossing totalled the amount of time an analogue signal was present in each 'level' and counted each time a level was crossed. The sequential peak and valley program recorded extreme values of the random analogue signal. Finally, the XY-intercept was employed to record the deflections of the rotor bearing as a function of the rev/min. The signal conditioner module of Datamyte 400 has a gain adjustable by discrete steps. The output of this unit represents the input to the true computer section of the Datamyte system. There are 64 'levels' between + 5 V and --5 V as defined at the computer input (see Fig. 4). However, only the voltage range of .+2.5 V was actually processed according to the programs mentioned above. This range was divided into 32 levels at the computer output, corresponding to -+3% resolution in the digital representation of the analogue signal. Nevertheless, the events on the levels 0 to 15 and 48 to 63 at the computer input were not entirely discarded. The number of valleys and peaks in these levels were counted and those counts were part of the Datamyte output to the printer. The present series of experiments were all made with a gain factor of 7500 across the signal conditioner. The model system and the conditioner were calibrated so that a deflection of the spring-mounted bearing support of •+0.85 mm corresponded to the full measuring range, that is to levels 0 and 31 at the computer output. The Datamyte has two kinds of filters: the signal conditioner contains an analogue low pass filter which is factory set at approximately 250 Hz at -- 3 dB; there is also a 'digital filter' referred to as an 'adjustable hysteresis'. For example, if the hysteresis input is set at HYS 5 with the rainflow program, all range counts of magnitude of ~"'~. levels or less are suppressed and do n o t appear at the computer output. As a separate complement to the Datamyte recordings, the amplified analogue signal available at the output of the signal conditioner was studied with a Brush pen recorder.
ResuIts Rain flow recordings
Fig. 3 A close up of the r o t o r showing the t w o sensor systems
146
The real-time rainflow algorithm has already been described elsewhere. 1 One rainflow range count is demonstrated in Fig. 4, where it stretches over ten levels, ie 10/32 parts of the 'full scale output'. Eighteen rainflow runs were undertaken according to the procedure just described. The output signal was observed with a digital voltmeter at the complete stop after each run. One of the eighteen recordings was discarded because its final static reading was considered to deviate too much from the initial setting before the run, ie by some 10% of the full output scale defined in Fig. 4. The scheme used to give some degree of statistical confidence in the results was as follows. For every one of
Int J Fatigue July 1983
+2 x Full scale
To computer
From computer
Input bond definition
Output bond definition
65
8 +2.5V
+ Full scale
Tension direction Signal conditioner
!=
,Gain7 5 0 0 ~ ' J
-
+Full scale
t Zero
Compression direction
+5V
51 52
I
0V
16
i
- 7,~,,~T Rainflow range
I
-Full scale
16 15 -2.5V
(3
- -Full scale
DC volts at output of signal conditioner
-2 x Full scale
0
-5V
Fig. 4. Definitions of signal gain, computer input and output levels (bands), showing one rainflow range count of magnitude 10 levels
the three configurations B0, B1 and B2 four consecutive runs were recorded. These were intended to establish a possible 'normalcy' at each level of rotor imbalance (0, 0.15% and 0.30%). The behaviour of the B1 rotor was studied by purring the output of the Datamyte signal conditioner module into the input terminals of a Brush Mark 280 pen recorder. The Datamyte was set at maximum gain and the recorder adjusted to a sensitivity of 2 mV/line and a paper speed of 50 mm/s. The results are shown in Fig. 5. Fig. 5a shows the onset of double critical shaft speed vibration at 3800 rev/min. The beginning of shaft critical speed vibration at 2000 rev/min is shown in Fig. 5b. Fig. 5c shows the passage through the low speed bearing support vibration at 500 rev/min, the maximum amplitude of which corresponds to about -+1 mm displacement amplitude of the bearing support. The recording of the balanced configuration, B0, and that of the most unbalanced, B2, may be compared. For both, the hysteresis setting HYS 5 suppressed all range counts below or equal to five levels of magnitude (see Figs 6 and 7). These recordings reveal obvious differences in behaviour. Firstly, it can be noted that the total number of range counts for the balanced rotor is 334 and for the unbalanced no less than 1889. Secondly, there are far more range counts of large magnitude for the unbalanced rotor. The balanced rotor had only 20 counts whereas the unbalanced one had 249 counts. Thirdly, besides the range counts, the Datamyte records the peaks and valleys in the input side bands 4 8 - 6 3 and 0 - 1 5 respectively. The balanced rotor had none, the unbalanced 34 peaks and 49 valleys in those bands. This means that the flexible bearing support was deflected more than 0.85 mm out of the static no-run position. R a i n f l o w damage i n d e x
Socie 1 has discussed life estimation techniques from rain-
Int J Fatigue July 1983
flow counted histograms and has distinguished between load or stress life analysis and strain life analysis. The fatigue life is based on the sum of the fatigue damage, Di, experienced for each load range, where D i = N/Nf. Here N is the number of rainflow range counts and Nf is the number of cycles to fatigue failure at any given constant amplitude. In this concept of linear cumulative damage, the total damage D is:
D : ~ D i = ~. (N/Nf) i i
i
It is also considered that D = 1 corresponds t o the most
probable fatigue life. This assumption has been frequently criticized although nothing better has been proposed in connection with the present techniques of measuring fatigue in mechanical engineering. The load-life approach applies to cases where the actual component is being tested rather than a laboratory specimen. An equation of the following form has been shown to fit fatigue data: A p -- p'(2Nf)m where Ap = load range = constant x R; R = rainflow range; and m =--0.2223. The present project is motivated by the hypothesis that a fatigue life monitoring scheme should be based on the cumulative damage theory. However it was not considered necessary at this stage to scale the rainflow damage index so that D = 1 would be a precise final alarm. In other words, the linear scale factor could be more arbitrarily assigned. From the above relationship (Ap =f(Nf)), it may be written: 1 R = --" (Nf) -0'2223 k
or
Nf = (kR) -4"50
147
g. 5 The behaviour of the 61 rotor system: (a) double critical shaft speed vibration revlmin (c) low speed bearing support vibration at 500 revlmin
at 3800
rev/min
(b) shaft critical speed vibration
at
2(,bO
Assuming a series of constant amplitude experiments, so that DI = and assigning value 1 D for = 31 Nf = the following be obtained: = (0.006949 This value would give results calculated Table 1. physical motion the bearing would be x 0.85 1.70 mm the rainflow count of This may compared with Bl configuration with the pen recorder. maximum low vibration amplitude to a count of tude 2 Table 1 demonstrates the of large ranges in damage index. above formulae applied to Datamyte recordings. each individual set of and rainflow counts, a value was by the of the = f(R) The D ZDi values plotted in 8.
148
D
from 0.032
0.0665 based
four runs
each
rotor A second of five (BO, Bl, 82, B2) an almost relationship between and the imbalance. In the relatively D value the balanced was not in this round of Table 1.
values of
damage index Rainflow damage D
Rainflow counts,
Nf 1 000 7189
1000 1000
1 00 0.13900 15
10
Int
Fatigue
July
DATAMYTE 451-23
-
RI--AL--rIMER(IIN FLOW T:IME: 0,1 d:[R X 01
rEST N A M E ~ 4YS= 5
IDI2D=I
SHUTDN OFLOW 0
T:[ME SWO
29
0
>+FS 0
0
SWI
SW2
0
0
<-FS +2*FS -2*FS +PEAK -F'EAK 0 O 0
RANGE COUNT FULL CYCLES .
.
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.
the extreme levels 1, 2, 3, 29, 30 and 31 were counted for a number of runs as shown in Table 2. Even though it may be argued that the counts of level crossings should be made over an equal time period, it could be counter-argued that the runs all covered the same passage through three critical speeds. i)AT,~HY[E .~51-23
HIS= 5
i~!Ii~ x :)i
IDx2D=I
SHUTDN OFLOW TIME 0
.
.
00000000
Fig. 6 Rainflow data for BO rotor
0
(~
<-FS +2*FS -=.~F,.~ +F'F-'AI(-PEAl< 17 62 I 49 2
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18 00000109 17 00000024
Provided that a larger number of samples for the 'normal' condition of real, full scale machines are used, the damage index D could be a trustworthy single parameter index to m o n i t o r deterioration of the dynamic behaviour. Balanced rotors would always give a rather low index, whereas an increase in the index after a certain time of operation would indicate worse conditions and the onset of fatigue and wear.
I;:.~ 00000039 19 00000005
20 OOO00005 21 00000004 22 00000004 23 OO00000J
24 O00000oi 25 00000004 22 ou,:)O0002
Time-at-level and level crossing recordings
The number of crossings (over more than nine levels) to
..%
0
6 000002,59 7 00000328 i~ 00000104 9 00000168 10 00000124 I I 00000171 12 00000107 1:3 00000118 14 00000058 15 00()00198
00000001
Level crossing index, LCI
0
27
RANGE COUNT FULL CYCLES .
00000001 00000010
The time-at-level and level crossing program totals the amount of time an analogue signal is present in each of the 32 levels of the computer output, as presented in Fig. 4. The program also counts each time one of the 32 levels is crossed (entered) and it stores the counts for each level. Thirteen runs were recorded for the three rotor configurations to examine if level crossing counts could perhaps be used for a single parameter index similar to the rainflow damage index. All o f the level crossing recordings were made at maximum suppression of the smaller scale level crossings, so that no level crossings equal to or less than nine levels between a peak to the next valley or vice versa were recorded; this appeared to be the best f o r m a t for the indication of abnormal conditions. The balanced B0 rotor and the unbalanced B2 were recorded as shown in Figs 9 and 10. Fig. 9 shows that the flexible bearing deflection was very moderate and close to zero, since it stayed on levels 13, 14 and 15 for 87°,/0 of the time. The unbalanced rotor spent 60% o f its time in close-to-zero conditions. Furthermore, level crossings over more than nine levels to or from levels 1, 2 and 3 or 29, 30 and 31 respectively were considerably more numerous for the unbalanced rotor.
0
?+FS 34
12 00000008
Int J Fatigue J u l y 1983
(I[ME.: 0.1
iES~ ~ A M E ~
.
6 00000167 7 00000087 8 00000028 9 00000007 10 00000002 11 00000006 12 00000002 13 00000005 14 O0000001 15 00000009 113 19 20 31
rq:iAl_-TlJ~iE R~.IN Fi O!,J
-
2!.-,' 00000004
2q 00000004 30 00000004
L(I 00000037 4: Fig. 7 Rainflow data for B2 rotor
? 0
c3
6 5
o
E
o
4
o•
2
I o
9
O
I
i
I
2
i
3
Irnbolonce (%) Fig. 8 R a i n f l o w damage i n d e x , D as a f u n c t i o n o f relative r o t o r i m b a l a n c e : o average values o f f o u r tests f o r each r o t o r i m b a l a n c e , o sample tests a f t e r establishing t h e average values
149
Table 2. Variation of level crossing counts with rotor imbalance
Rotor
BO
81
B2
Number of level crossings (over levels 1 , 2 , 3, 29, 30, 31 )
Time duration of run (min)
Average counts o f level crossings
3.2 3.4
13
297 321
3.3 3.2
314
1331 415 171 343
2.2 2.4 2.7 2.5
565
HYS:9 TEST NAME [002 TEST BEGUN
-
T;[ME-AT-LEVEL + LEVEL CROSSING
TEST NAME TO02
TIME: 0.1 M~N X 01
HYS= 9 SHUTDN OFLOU TIME SWO 0 0 32 0
SWI 0
BIN COUNTS COUNTS% NO. AT 800 0 000000000024 000.01% I 000000000013 000,00% 2 000000000105 000.06% 3 000000000143 000.09% 4 000000000157 000,I0% 5 000000000185 000.11% 6 000000000225 000.14% 7 000000000249 000.15% 8 000000000365 000.23% 9 000000000530 000.34% 10 000000000791 000.50% 11 000000001837 001.17% 12 000000007726 004,96% 13 000000032968 021.16% 14 000000077529 049.78% 15 000000024984 016.04% 16 000000003581 002.29% 12 000000001645 001.05% 18 000000000852 000.54% 19 000000000432 000.27% 20 000000000380 000.24% 21 000000000276 000.17% 22 000000000192 000.12% 23 000000000149 000.09% 24 000000000157 000.10% 25 000000000128 000.08% 26 000000000096 000.06% 27 000000000002 000.00% 28 000000000002 000.00% 29 000000000004 000.00% 30 000000000004 000.00% 31 000000000011 000,00% TOTAL COUNTS 000000155742
SW2 0 LEVEl_ CROSSING 0000000~ 00000003 00000014 00000030 00000042 00000054 00000068 00000083 00000102 00000123 00000131 00000131 00000131 0000013I 00000131 00000131 00000131 00000132 00000132 00000122 00000101 00000078 00000060 00000049 00000039 00000029 00000013 00000002 00000002 00000002 00000002 00000001
Fig. 9 Time-at-level and level crossing data for BO rotor
150
:~:F'
DATAMYTE 454-11
TIME-AT-LI-VEL ÷ LEVI-L CI~OS!~INI
FEST NAME TOIl
23 2
*F' DATAMYTE 454-11
H¥S= 9 [EST NAME T011 fEST BEGUN
rIME: O.l
M:[N X Ol
IIYS= 9 SHUTDN OFLOW TIME 0 0 24
S~O 0
SW1 0
SW2 0
BIN COUNTS COUNTS% NO. AT 800 0 000000000683 000.61% I 000000000161 000.14Z 2 000000000223 000.19% 3 000000000314 000.28% 4 000000000575 000.51% 5 000000000955 000.85% 6 000000001246 001.11% ? 000000002070 001.84% 8 000000002996 002.67% ? 000000003537 003.18% 10 000000004685 004.18% 11 000000004362 003.89% 12 000000005673 005.06% 13 000000007467 006.67% 14 000000016592 014.82% 15 000000034346 030.68% 16 000000008387 007.49% 17 000000006285 005.61% 18 000000004245 004.23% 19 000000002351 002.10% 20 000000001643 001,46% 21 000000000935 000.83% 22 000000000537 000.47% 23 000000000327 000.29% 24 000000000181 000.16% 25 000000000071 000.06% 26 000000000063 000.05% 27 000000000040 000.03% 28 000000000045 000.04% 29 000000000039 000.03% 30 000000000042 O00,03X 31 000000000339 000.30% TOTAL COUNTS 000000"111915
LEVEl_ CROSSI[NG
00000036 00000113 00000189 00000269 00000416 00000653 00000902 00001182 00001522 00001720 00001875 00002'125 00002291 00002322 00002322 00002322 00002316 00002274 00002051 00001202 00001347 00000942 00000573 00000294 00000126 0000005? 00000041 00000037 00000035 00000033 00000030 00000014
Fig. 10 Time-at-level and level crossing data for B2 rotor
Therefore the average of counts obtained for the three configurations was seen as a relevant index. To obtain an index similar to the rainflow damage index, the following was used: LCI -- (average count)/10 000 Fig. 11 shows that there is an almost linear relationship between LCI and the percentage imbalance. The wellbalanced rotor exhibits an extremely low LCI. Also, even a slight imbalance consistently raises the LCI significantly.
Sequential peak and valley recordings The sequential peak and valley program provided a very distinct and different record for the tested rotors with respect to their degree of imbalance. This program is the only one in the study which has a partial flavour of the time variable, since it records the extreme high and low
Int J Fatigue July 1983
5
~o
6
4
0
I
0
I
I
2 Imbolonce (%)
1 3
Fig. 11 Level crossing index, LCI, as a function of relative rotor imbalance. LCI is counted for bands 1,2, 3, 29, 30 and 31 DATAMYTE 452-04
SEQUENTIALPEAK-VALLEY
TEST NAME SS003
BEG. HYS=09 ISHUTDN OFLO~ 0
>+FS 0
0
TIHE: 0.1MIN X Ol END HYS=09
TIME
S~O
Sgl
0
0
29
5~2 0
K-FS +2*FS -2*FS +PEA~C-PEA~( 0
0
this program with 16 deflection columns. The rev/min pulses (2 per rev) are resolved into a maximum of 32 bands for 300 Hz. Running the rotor at 4000 rev/min thus corresponds to 4000(2/60) (32/300) = 14 bands or rows in the Datamyte print. Most of the readings are concentrated in columns 7 and 8 which correspond to small or zero deflection. Also, each count in Fig. 15 represents the average value over 0.427 seconds. The extreme deflections, as already recorded by the previous programs, do not usually last that long. Therefore the XY-intercept is most useful in monitoring slightly more permanent characteristics. The different passage phases may easily be detected in Fig. 15. The supercritical speed counts are concentrated in column 8. The critical shaft speed (around 1500 rev/min) moves the counts into columns 6 and 7, whereas the rows 5, 6 and 7 correspond to a speed range between 1400 and 1970 rev/min. In row 1, ie 280 rev/min and below, a count in column 5 occurs, which represents the passage into the low speed large deflection phase. A double number of pulses for each revolution would have improved the present rev/min resolution with this program. However it has been sufficiently demonstrated that the program provides a frequency response, though averaged, both with respect to each cycle and to the longer time average.
0
PEAK AND VALLEY DATA
20,I0,20,09,20,09,20,09,20,09,20,09,20,09,20,0!3,20,08,20,08 20,08,21,08,21,07,21,07,21,07,21,07,22,07,22,06,22,06,22,06
DATAMYTE 4 5 2 - 0 4
23,06,23,06,23,05,23,05,23,05,24,05,24,05,24,05,24,05,24,04
TEST NAME S002
24,04,24,04,25,04,25,04,25,04,25,04,25,04,25,03,25,03,25,03 25,03,26,03,26,03,26,OJ,26,03,Z6,04,25,04,25,v4,25,05~25,05 24,05,24,06,23,07,22,08,21,08,21,09,20,10,20,~0,20,10,20,10 20,09,20,I0,20,09,20,10,21,09,20,09~21,09,20,09,2~,09,20,'I0 21,09,20,10,21,10 Fig. 12 Sequential peak and valley data for BO rotor. The test was run w i t h m a x i m u m i n i t i a l
hysteresis
BEG, HYS=O9
SEQUENTIALPEAK±VALLEY TIME: 0.I RIM X 01
END HYS:I3
SHUTDN OFLOg TIME SgO 0 0 26 0
Sgl 0
Sg2 0
>+FS <-FS +2*FS -2*FS +PEAl.( -PEAH I? 30 3 ? 62 1 PEAK ANO VALLEY OATA
values of the deflection transducer sequentially. This facilitates the study of the actual dynamic behaviour of the rotor system. The balanced B0 rotor is represented in Fig. 12. Since the initial 'hysteresis' is set at the maximum value of nine bands, all the smaller deflections are left unrecorded. This could be helpful in the case of monitoring, whereas a study of fracture mechanics would be conducted with zero hysteresis. The behaviour of the B2 rotor is described in Fig. 13 and graphically in Fig. 14. Despite the suppression of the smaller deflections the run exhausted the entire m e m o r y space of the Datamyte. On the left of Fig. 14, well above the critical speed, the rotor shows relative stability. The next two sequences correspond to the onset of larger amplitudes when passing through the shaft critical speed at about 1500 rev/min. At the right end of Fig. 14, it becomes clear that passage through the very low speed deflection of the support springs creates the most severe load on the system. This effect was not distinguished by the other programs.
10,24,10,24,10,24,10,24.09,24,09,24,09,24,09,24,09,25,0%25
09,24,09,25,09,25,08,25,08,25,09~25,08,25,08,25,08,25,08,25 oe,26,o8,26,o8,26,o8,26,o8,26,o8,26,08,26,08~26,08,26,08,28 08,27,08,26,08,26,08,26,08,26,08,27,08,27,08,27,08,27.08,27 08~27,08.27,08,27,08,27~08,27,08~27,08,27~08,27,08~27~08,27 08,27,08,27,08,27,08,27,08,27,08,27,08,27,08,27,09,27,09,27 09,27,09,27,09,27,09,27,08,27,09,27~09,27,09,27,09,27,09,26 09,26,09,27,09,27,10,27,10,27,09,26,09,26,09,26,09,27,I0,27 10,27,10,26,09,26,09,26,09,26,09,26,10,27,10.27,10,27,10.26 "10,26,~0,26,10,26,t0,26,10,26,10,26,~0,26,10,26,10,26.10,26 II,26,11,26,11,26,1I,26,II,26 II,26,11,26,11,26,1"I,26,Ii,26 I 1,26, 11,2,:~,I1,26,11,26,11,26,11,26 i 26,II,26,II ,~6,12,26, ~ -1 ,i ,~ 9 ~ 9 9' 1 2 , 2 6 ,~6,1~,~6,I I ,26,I 1,26,11.26,
10,.6,11 ,.6,11,26,11,26,11,26, ,26,11,26,11,26,11,26,11,26,
2,26,12,26,1~,.6~° .~ 12,26,12,26, . : ~6,1 . , , ~ 6 , I ~ ~.~8, 1 2 , 2 6 , 1 2 , 2 6 ,
12,26,12,26,12,28~12,28,19
?~i
12,26,12,2~,12,2~,~2,26,1::2;I
2,26,12,26,12,26,12,26,12,26, 06,20,06.20~06,20,08,20,06,20 06,20,06,20,06,20,06,20,06,20, 0a,~0,0~,.0,05,.0,06,~0,05,-0i 06,20,05,20,06,20,05,20,06,20, o~,~o,o~;~o;o5;~,o5,~,o5,~o 05,1q,05,20,06,20,05,20,05,20,06,20,05,19,05,20,05,20,05,20 05~20~05,19,05,19,05,19,05,17,05,19,05,1%05~19~05,17,05~19' 05,19~05j19~O5,19,05~lg~OS,19,05~lgy05,1%05~20,05~21~07,21
07,21,07,21~07,21~07,21,07,21,07~21,01,22,07,22,07,22,07,22 07,22,07,22,07,22,06,22,06,22,06,23,06,22,06,22,05~23,05,23 05,23,05,23,05,23,05,23,05,23,05,23,05,23,05,24,04,24,04,24 04,24,04,24,04,24,04,24,03,24,03,24,03,25,03,25,02,25,02,25
Time a t X Y-intercept recordings
02~25,02,25,02,25,02,26,01,26,01,26,01,27,00,22,00,22,00,22
In this program, the load variable (deflection) is limited to 16 bands for the full scale deflection, so all the values for deflection should be doubled for comparison with those of the other programs. Fig. 15 for a B2 rotor demonstrates the format of
00,31,00,31,00,31,00,31,00,31,00,31,00,31~00~31~00,31~00,31
Int J Fatigue July 1983
00,28,00,28,00,28,00,28,00,29,00,29,00,2%00~30,00,30,00,31 00,31,00,31,00,31,00,31,00,31,00,31,00,31,00,31,00,3'1,00,~1
00,31,02,28,04,26,06,25,07,25,07,25,07,25,07,25,07,25,07,24 08,24,08,24,08,24,09,23,09,23,09,23,09~23,09 Fig. 13 Sequential peak and valley data for B2 rotor. The test was run with maximum initial hysteresis
151
L
I:=, soo2
3°I
1 82• ,
I ,
I
=
e c- 2 0
8 ==
....
-o
L--C_
g io
dSUperc 0 F i g . 1 4 D i s p l a y o f digital data from sequential peak and valley program. The time variable has been simplified to give equal distance between the peaks over the whole region
DATAMYTE
E1ME-AT-XY- IN'[ERSEC[S
455-06
TIrME: 0.1 MIN X 01
lEST N A M E ~ 9HUTDN 0 ROg NO.
OFLOW
TIME 0
COLUNNS 0
25
ROTOR
SPEED
DEFLECTION
I
2
3
4
5
12 13 51
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0,1500 0 0 0 0 0 0 0 0 4000 O"
0 0 0 0 0 rpm 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
lOT
O0
O0
O0
01
00 01 02 03 04 05 06 O7 08 O? I0
II
O0
O0
?
8
9
0 0 ? 0 0 13 I? 1S 0 0 0 0 0 0 0
0 119 I ,54 2? 0 35 0 27 0 I 0 0 0 I 0 l0 0 4 5 0 9 0 6 0 8 0 4 0 0
0 0 0 0 0 0 0 0 0 0 ~ 0 0 0 0
49
106 205
O0
11
12
0 0 ,3 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
O0
O0
0,.
I0
13 0 0 0 0 ,) 0 0 0 0 0 0 ,:) 0 0 0 O0
14 0 0 0 0 ,) 0 0 0 0 0 0 0 0 0 0 .)0
115 0 0 0 0 ', 0 0 0 0 0 ,i ,3 0 0 0 Ov
TO IAI. i I':~ !~6 31 3'~ 2? ]4 I: I3 10 ,~ ,37 9,:~ 0 04 ,:~:, 3~]
F i g . 15 T i m e at the X Y intercept for B 2 r o t o r
Design of a monitoring system
•
Once the feasibility of a single parameter index for a given machine system has been established, the actual design of a complete monitoring instrument may be considered. In particular, the following points should be considered:
•
•
Is it desirable to have more than one sensor and therefore to arrange for scanning with a multiplexer that connects the Datamyte to two or several sensors in a sequence?*
* I t has been suggested that one ought to use a multichannel device. A t the time of this research project, no such devices were on the market at a reasonable price. Even if several systems are arranged in one frame, they still constitute that many separate microcomputers.
152
• •
•
To what extent would it be desirable to save more permanently the recordings taken during any time interval? How long should each transducer be connected to the Datamyte: 10 000 or 1000 seconds? What exact form of the index is most suitable? Should the collection of the originalvalues of 'normal' conditions be an integrated, automated sequence of monitoring equipment? What hardware configuration would be best for more permanent memory storage?
When the answers to the above questions are better known, the monitoring system can be designed. The objectives of the design would preferably be an effective low cost
Int J Fatigue July 1983
Parallel interface
I
Transducer
I
ALU
~=~
RAM
zE~Operotionoi E ~ amplifiers i
r=L interface
i
Address bus
Fig. 16 Possible design of Dynalog system for condition monitoring of machine systems. The address bus communicates signals to the transducer multiplexer to switch the desired transducer channel to the histogram recorder and looks up the permanent memory for individual fingerprints. The executive communicates with the histogram recorder (both addressing and data transfer) via a standard EIA 232 serial interface
alternative, in line with the general philosophy of modem self-sustained histogram recorders. One example of the layout for the monitoring equipment is illustrated in Fig. 15.
Conclusions Using an inexpensive laboratory model a preliminary
Int J Fatigue July 1983
investigation into the use of histogram recorders for monitoring mechanical vibrations has been made. The results should only be considered as indicative and are intended to serve as guidelines for the design of real life equipment. All tests were duplicated several times for observation of consistency in the data and in the return to static readings after each complete stop. However, the number of tests for each case was not large enough to establish statistical parameters with any acceptable degree of confidence. On the other hand this was not necessary in order to verify the basic hypothesis that both real-time rainflow and the level crossing programs should provide a basis for a single index to detect early tendencies of deterioration in dynamical behaviour. The peak and valley and the XY intercept programs supported the data of the first two programs and provided useful, complementary information about the model.
References Socie, D. F. 'Fatigue life estimation techniques' Technical Report No 145 (Electro General Corp, 1981)
Author Professor Schnittger is with The Royal Institute of Technology (KTH), Department of Machine Elements, Brinellv~gen 68, S-10044 Stockholm, Sweden.
153