CHAPTER 4 WEIBULL ANALYSIS

Transcription

1 48 CHAPTER 4 WEIBULL ANALYSIS 4. INTRODUCTION Weibull analysis is used o analyze he daa from all phases of produc life. The Weibull disribuion is one of he mos exensively used lifeime disribuions in reliabiliy engineering and is he mos useful probabiliy disribuion. The primary advanages of Weibull analysis are having he capabiliy o provide reasonably accurae failure analysis, and failure forecass wih exremely small amoun, and i affords a valuable graphical plo of he failure daa. I is a flexible disribuion ha can ake on he characerisics of oher ypes of disribuions, based on he value of he shape parameer,. An imporan characerisic of he Weibull disribuion is how he values of he shape parameer,, and he scale parameer,, affec he reliabiliy and he failure rae. The main objecive of his research using Weibull analysis is o increase he efficiency of generaion by idenifying he failure rends, esablishing benchmark for reliabiliy performance and providing excellen informaion o operaion and mainenance eam o make precauions. The earlier research [ =] assumed ha he consan failure rae for calculaing reliabiliy of onshore wind urbines, bu some componens like generaor, yaw moor and brake sysem failed rapidly. I shows ha he assumpion of consan failure rae is no longer valid. In his research, mechanical sub assemblies are mainly considered because hey are affeced heavily by

2 49 dynamic loads due o frequen change in he direcion and wind velociy a normal operaing period. In he modern age, he higher reliabiliy requiremen sysems are geing complicaed because of conrol sysem, compuing sysem mulisage inerconnecion and criical power sysem. This complexiy causes frequen failure in he wind urbines. The wind power sysem is comprised of one or more unis, operaing elecrically in parallel, having he following componens such as he ower and conrol sysem, roor sysem wih blades, hub, nose cone and ip mechanism, yaw mechanism, gear box, elecrical generaor, brake sysem, he speed sensors and conrol. The modern sysem ofen has he following addiional componens such as power elecronics and wireless conrol incorporaing a cenralized conrol. 4.2 WEIBULL ANALYSIS OF WT Weibull analysis includes ploing he daa and inerpreing he plo, failure forecasing and predicion, evaluaing correcive acion plans, mainenance planning and cos effecive replacemen sraegies, spare pars forecasing, warrany analysis and recommendaions o managemen in response o service problems Weibull analysis provides he life daa analysis ools necessary o analyze daa from all phases of produc life. The inuiive inerface ools ogeher wih a comprehensive selecion of plos and graphs enable o predic failure behavior. The weibull disribuion is used o model boh increasing and decreasing failure raes. I is characerized by a hazard rae funcion of he form is given in Equaion (4.). () = a b (4.)

3 50 And i is he power funcion () is increasing for a 0, b 0 () is decreasing for a 0, b 0 Obviously he probabiliy is 0 a = 0 and increases monoonically o as goes o infiniy. The corresponding densiy disribuion f () is he derivaive of his cumulaive probabiliy funcion (cdf). This enables us o define a probabiliy densiy funcion (pdf) wih any specified rae funcion as given in Equaion (4.2). f e (4.2) Weibull analysis sofware provides he life daa analysis ools necessary o analyze daa from all phases of produc life. The inuiive inerface ools ogeher wih a () 0, 0 or, > 0, > 0, < < = characerisic life or Scale parameer = Slope parameer or Shape parameer = Failure free life or Locaion parameer. The deermines he rend of he curve and i is called shape parameer. The is a scale parameer which has unis of he reciprocal of ime and is he locaion parameer. For < or > he curve shows respecively a downward or an upward rend. The parameer is a

4 5 dimensionless pure number. The failure of WT componens are calculaed based on field daa by using Weibull sofware. The Weibull cumulaive densiy funcion (cdf) F () or Unreliabiliy for hree parameers is given by Equaion (4.3). F e (4.3) by Equaion (4.4). Then he reliabiliy of he hree parameer Weibull funcion is given R e (4.4) By definiion MTTF can de wrien as Equaion (4.5). M T T F 0 e d (4.5) Le y y (4.6) Then d y d (4.7) or M T T F 0 e y d y (4.8) Since y y / M T T F 0 y e / y d y (4.9)

5 52 M T T F. (4.0) is he gamma funcion Similarly he median and mode are derived as Equaion (4.9) and (4.0). M e d ia n.(ln 2) (4.) Mode. (4.2) Weibull failure rae funcion is specified by Equaion (4.3). f ( ) R ( ) (4.3) The Weibull plo shows he onse of failure, i may be of ineres o deermine he ime a which % of he populaion would have failed and is called he "B" life. For more serious or caasrophic failures, a lower risk may be required. The desired reliabiliy R is prearranged by Equaion (4.4). R e R (4.4) The design life is prearranged by Equaion (4.5). R ( ln R ) (4.5)

6 53 When R= 0.99 is referred as he B life. The B life is defined as ime a which % of he componens have failed. 4.3 FAILURE DISTRIBUTION OF WT COMPONENTS The failure of WT componens are calculaed based on field daa by using Weibull analysis. The failure disribuion daa is shown in he Table 4.. Table 4. Failure disribuion of WT Componens Componen Number Componen Name Failure Disribuion C Roor Weibull ( =.8257, =84678, =0.9237) C2 Gear box Weibull ( =.2327, =6622, =0.974) C3 Brake Sysem Weibull ( =.7459, =82942, =0.9667) C4 Generaor Weibull ( =0.7653, =59252, =0.8566) C5 Yaw Sysem Weibull ( =.8665, =58930, =0.99) C6 Hydraulic Tip Conrol Weibull ( =.027, =78273, =0.9553) C7 Hydraulic Brake Conrol Weibull ( =.6059, =89672 =0.9455) WTS Weibull ( =.2639, =7004, =0.9039) 4.3. The Effec of on he Weibull Failure Rae of WT The value of has a disinguished effec on he failure rae of he Weibull analysis and inferences can be drawn abou failure characerisics by considering wheher he value of is less han, equal o or greaer han one. In

7 54 his research, he shape facor values obained are greaer han for all componens excep generaor. The failures are rapid and random for all componens and i will deeriorae due o faigue load and dynamic load. The roor has value of The failure rae increased wih age and i indicaes ha he roor was brough ino service soon. The roor failure is due o roor main bearing failure, bol failure and dir in he blades. The main reasons for he roor failure are heavy vibraion, wind urbulence, poor blade maerial and mechanical failure and i occurs during high flucuaion in wind. The majoriy of WT gear box failures appear o iniiae in he bearings and shaf. The gear box has a value of.2327 and he failure is due o random cyclic loading and emperaure changes. The brake sysem has a value of.7459 and is due o acceleraed wear. The causes of failure are sochasic. The failure of brake is major, and is due o frequen worn ou of brake pads. The generaor has a value of I clearly illusraes ha incredibly frequen failures occur high righ from infan moraliy period. The is less han, he decreasing failure rae indicaing high infan moraliy having a low safey margin. I gave rise o sress rupure failure. If he wind speed changes beween average wind speed (9 m/sec) and below raed wind speed ( m/sec), hen he conacor for generaor G and generaor G2 acuaes frequenly and makes he generaor fail. Mos of he generaors are over hanging herefore he bearing and shaf of generaor habiually fail. The hydraulic conrol of he roor has a value of.027 and i is ime independen failure. The sources of hydraulic conrol of he roor failure are malfuncion of mechanism and process error, which resuls in he ip opening while operaion and blade rope cu.

8 55 The hydraulic conrol of he brake has a value of.6059 and i is age relaed paern of failure. The failure of oil seal, hydraulic pump, hydraulic hose and hydrosaic spring made he value larger The Effec of and on he Weibull Failure Rae of WT The scale parameer deermines he range of he disribuion. The scale parameer is also known as he characerisic life if he locaion parameer is equal o zero for wo parameer- Weibull disribuion. If is no equal o zero, he characerisic life is equal o % of all values fall below he characerisic life regardless of he value of he shape parameer. The is he failure free life or locaion parameer. The locaion parameer is principally used o define a failure-free zone. The characerisic life for generaor, yaw and gear box is 59,252 hours, 58,930 hours and 66,22 hours, respecively and hey are low because of frequen failures. The values for hydraulic brake conrol and roor are 89,672 hours and 84,678 hours because of less frequencies of failure. The locaion parameer >0 is highly reliable bu, he locaion parameers are below one. The value of for roor is and i denoes ha he roor suffered a failure of 7.63%.The value of for generaor is and is oo low and requires immediae acion. The locaion parameers of gear box, brake sysem, yaw sysem, and roor hydraulic sysem are 0.974, , 0.99and respecively. 4.4 FAILURE RATE (UNRELIABILITY) The failure rae () is he frequency wih which a sysem or componen fails wih paricular ime. The failure rae is he raio of he probabiliy densiy funcion of failure a ime f () and reliabiliy wih a funcion of ime R () as given by Equaion (4.).

9 56 I is an imporan ool in deermining he appropriae probabilisic model for a se of daa. By appropriaely ransforming he failure ime values, he exac qualiy of finess ess can be consruced for he model. The unreliabiliy funcion is also called he failure disribued funcion. Figure 4. Probabiliy disribuion of WT failure The Figure 4. illusraes ha he recorded values are closer o sraigh line a iniial sage and final sage of he Weibull plo, which indicaes he qualiy of finess of Weibull disribuion. The poins are he acual values aken from field daa. The failure densiy is low up o 20,000 hours and medium up o 60,000 hours. Afer ha, he failure densiy has increased. The plo of he daa looks like a sraigh line which can idenify he qualiy of finess of Weibull disribuion. The daa fi will ell us he Weibull is good enough. The Figure 4.2 is a plo of he failure rae over ime and illusraes a considerable amoun of failures occurred in infan moraliy period ha is below 0,000 hours. In beween 0,000 and 30,000 hours, he failure is very

10 57 less. Afer, 00,000 hours, he failures are massive. I varies from o failures per hour. Figure 4.2 Probabiliy Failures of WTS I is revealed ha, he failure of he sysem depends on ime. If he ime is increased hen he failure rae is also increased. The life of he WT is generally designed for 25 years bu i is reduced o 20 o 22 years in acual pracice PROBABILITY DENSITY FUNCTION OF WTS WITH TIME The probabiliy densiy funcion of WT and is sub assemblies are shown in Figure 4.3. A saisical measure ha defines a probabiliy disribuion for a random variable and i describes relaive likelihood for random variable. I is denoed as f(x). The probabiliy densiy funcion is ofen used in he creaion of modeling for forecasing purpose and models he sysem and o faciliae more complee picure regarding fuure.

11 58 Figure 4.3 pdf of WTS wih ime The probabiliy densiy funcion has been ploed for 25,000 hours and 50,000 hours. The enire componens apar from generaor have increased o value of probabiliy funcion and i designaes ha he normal curve of he generaor sysem has less mean and i implies less efficien. 4.6 FAILURE RATE OF WTS WITH TIME The failure rae of WTS and is componens are shown in Figure 4.4. The roor, brake sysem and hydraulic conrol of brake sysem had less failure raes in 25, 000 hours as failures/ hour, failures/ hour and failures/ hour. The generaor had an iniial failure rae of failures/ hour and laer a failure of failures/ hour. This signifies ha he generaor has failure of infan moraliy and i requires immediae replacemen.

12 59 Figure 4.4 Failure rae (failures/ hour) of WTS wih ime 4.7 DESIGNED LIFE BY DESIRED RELIABILITY By calculaing he design life of he WT componens by adoping desired reliabiliy of 95% feched as resul, which describes he componens gear box, generaor and roor hydraulic sysem suffers a deficiency ( hours, hours and hours) in designed life when analysis is done for a period of 25,000 hours. Bu, he oher componens such as roor sysem ( hours), brake sysem ( hours), yaw sysem ( hours) and brake hydraulic ( hours) have a nominal deign life when he analysis is done for 25,000 hours. The sysem s overall design life is found o be hrough analysis. 4.8 B LIFE OF WT COMPONENTS The B values are used for design requiremens. In reliabiliy B life is used for benign failures, B 0. for serious failures and B0.0 for caasrophic failures. Here B failures are considered aking care on equipmens. I is a measuremen of he ime by which one percen of a populaion of a produc would have failed. The B life of all componens of

13 60 WT is shown in Table 4.2. The generaor has very less B life as hours. This is owing o incipien failure of generaor. The incipien failures ensued in he generaor are due o producion faul, assembly faul, cable faul, saor winding faul or roor mass imbalance, shor circui, coupling faul and bearing faul. The generaor ook long ime o sele down. Once he generaor was laid down for good generaion, and hen failures were minimized. Nex o generaor, he hydraulic conrol of he roor had a life of hours. The ip mechanism iniially faced heavy crisis and i had problem o open or close. The gear box has a B life of hours and i reveals ha he gear box had some failures iniially such as alignmen of roor, roor imbalance, nacelle angle, ower head level and improper assembly. The roor ( hour), Brake sysem ( hours), Yaw sysem (50.64 hours) and hydraulic brake conrol ( hours) had a subsanial B life. Table 4.2 B life of WT Componens Componen Number Componen Name B life Hours C Roor Sysem C2 Gear box Sysem C3 Brake Sysem C4 Generaor Sysem C5 Yaw Sysem C6 Hydraulic Tip Conrol C7 Hydraulic Brake Conrol WTS

14 6 4.9 WEIBULL RELIABILITY ANALYSIS OF WT COMPONENTS Reliabiliy analysis of WTS and is sub assemblies are depiced in Figure 4.5. This research analyzes he reliabiliy of differen componens which cause break down of he sysem and o idenify he criical failure occurred o make he sysem unavailable. In general, he failure rae of WT decreases wih ime bu he resul of his research shows ha rapid failure occurred in criical componens like generaor, yaw sysem, roor sysem, brake sysem and gear box. The ReliaSof s Weibull analysis sofware is used for he analysis o deermine he reliabiliy of WT componens. The reliabiliy is imporan because he wind urbines are mosly locaed in remoe regions where he cos of inspecions and repairs are very high. In a good high wind period a 250 kw WT can ypically produce abou 5,000 kwh per day. The maximum failures are obained in he high wind period only. The roor has a limied failure bu he resoraion ime is large. Therefore he reliabiliy of roor is very imporan. The faigue load, poor blade maerial and sress on he blade are some imporan reasons affecing he reliabiliy of roor. The low speed shaf is heavily affeced by uncerainy of he wind. Once load on he low speed shaf is irregular hen he bearing is affeced primarily and his disseminaes problem in he gear box. The bearings are failed due o debris damage. The rise in emperaure of gear oil, oil piing, and misalignmen of shaf leads o rouble. The brake sysem is he acive par of he proecion sysem of wind urbines. The reliabiliy of a brake sysem is of he umos imporance o ensure ha he sysem will serve is purpose effecively. The frequen usage

15 62 of brake o reduce he speed, over speed and abrup grid failure a high wind causes failure in he brake sysem as shown in he Figure 4.5. The G and G 2 conacor failure, power cable damage, winding failure, volage flucuaion in he grid and sensor failure made he generaor breakdown. If he changeover of he generaor is from high speed generaor G o low speed generaor G2 hen he mechanical brake is applied and ip is opened o reduce he speed. The general objecive of a WT yaw drive is o direc he WT ino he direcion of he wind. I is clear ha he failure of yaw sysem makes heavy reducion in he power generaion. The mos common ype of yaw mechanism is based on a rolling slew ring bearing wih a cogged inner or ouer race and pinions driven by elecrical moors over high-reducion gear boxes. The frequen acuaion of he yaw sysem causes an exreme failure in yaw planeary gear, yaw bed bol, pinion, yaw brake and yaw moor hus causes frequen failure of yaw mechanism. The direcion of wind abruply changes wihin an hour a Muppandal sie locaed in he Aramboly pass. The ip of blade open slighly due o he low pressure developed in he hydraulic sysem and i makes reducion in power generaion. I is common ha he ip is open slighly while running and i reduces he generaion exremely. This ip opening is due o looseness of blade rope, he poor maerial of carbon shaf and pressure drop in he cylinder. The hydraulic conrol of he brake faced age relaed problem like wear ou of oil seal and hydrosaic bearing. The repairs o generaor, drive rain, hub, gear box and blades have ofen caused sandsill periods of several weeks.

16 Figure 4.5 Reliabiliy Analysis of WT and is Componens 63

17 64 The urbine availabiliy is a funcion of boh failure disribuion as well as repair disribuion of individual componens. The reliabiliy of he enire wind energy sysem is shown in Figure 4.5. The Table 4.3 shows ha he overall reliabiliy wih ime of WTS. Table 4.3 Overall Reliabiliy of WTS Sl. No Time (hour) Reliabiliy E-3 This research also indicaes how o preven he failure before occurring and recommends ha he wind urbines need no be designed as commonly for all onshore plan. They can be designed wih some modificaions o mee challenges of he heavy uncerainy wind in he mounain pass and hilly area. These modificaions are recommended in design sage such as he redundan yaw sysem wih sof yaw drives wihou yaw brake, redundan hydraulic sysem, he proper design o align he generaor and proper gear box cooling wih exended surface area o improve he reliabiliy and availabiliy of he wind urbines. In order o furher improve he reliabiliy of wind urbines, he prevenive mainenance a low wind period, spare pars a sie and high qualiy elecric and elecronic componens are necessary. Besides failure rae, he resore ime of he machines afer a failure is an imporan value o describe he reliabiliy of a WT.

18 SUMMARY The WTS is formulaed as Weibull model and is life and is reliabiliy are compued for 250 kw wind urbines. The finess of he daa is analysed in his chaper and found Weibull is good enough. A more surdy soluion is obained by defining hree parameers such as scale facor, shape facor and locaion facor. The model also provides a designed life and B life of WT o predic he reliabiliy of individual componen during design and mainenance phase.