FUNDAMENTALS FOR CONDITION MONITORING AND DIAGNOSTICS FOR DRIVING BUCKET WHEEL SYSTEM WITH OVERLOAD MECHANISM OF BUCKET WHEEL EXCAVATOR

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1 Nr 133 Prace Naukowe Instytutu Górnictwa Politechniki Wrocławskiej Nr 133 Studia i Materiały Nr Walter BARTELMUS* bucket wheel excavator, bucket wheel drive, vibration condition monitoring FUNDAMENTALS FOR CONDITION MONITORING AND DIAGNOSTICS FOR DRIVING BUCKET WHEEL SYSTEM WITH OVERLOAD MECHANISM OF BUCKET WHEEL EXCAVATOR The paper gives undamentals or condition monitoring and diagnostics or the driving bucket wheel system o a bucket wheel excavator, which is designed or operation in increased digging resistance o strata. The undamentals are given by development the characteristic requencies as: meshing requences, local ault reqencies, carrier requencies or planetary gearboxes and so on. 1. INTRODUCTION Condition monitoring and diagnostics o driving systems or bucket wheels o bucket wheel excavators given in igure 1 and 2 are described in papers (Bartelmus, Zimro, 2007; Bartelmus, Zimro, 2009a; Bartelmus, Zimro, 2009b; Bartelmus et al., 2010; Bartelmus, Zimro, 2008; Bartelmus, Zimro, 2010a; Bartelmus, Zimro, 2010b; Bartelmus, Zimro, 2011). In a presented paper one can ind undamentals or the condition monitoring o the new design o a gearbox system which drives a bucked wheel o a bucked wheel excavator. The scheme o a new system is given in igure 3. The characteristic dierence between design o systems given in igure 1 or 2 and 3 is that in system (ig. 3) is given an overload mechanism. The term o a complex and compound gearbox is explained in (Bartelmus, Zimro, 2010b). The system given in igure 1 consists o planetary stage with gears 1, 2, 3 and three cylindrical stages, gears rom 4 to 9. * Politechnika Wrocławska, Wydiał Geoinżynierii Górnictwa i Geologii, Instytut Górnictwa, Vibration and Diagnostic Scientiic Laboratory, pl. Teatralny 2, Wrocław.

2 6 W. BARTELMUS Z 2 Z 1 Z 3 Z 5 Z 4 Z 7 Z 6 Z 9 Z 8 Fig. 1. Scheme o complex gear system Fig. 2. Scheme complex gear system used or bucked wheel driving

3 Fundamentals or condition monitoring and diagnostics or driving bucket wheel system 7 Fig. 3. Scheme o driving system or bucked wheel o bucked wheel excavator with overload mechanism

4 8 W. BARTELMUS The system given in igure 2 transmits the power through the bevel stage and next by two dierent ways. The irst way is through the planetary stage 3, 4, 5 and a cylindrical stage 8 and 9. It should be noticed that the planetary stage is characterised by two degrees o rotation reedom, which gives the possibility to rotate a sun 3 and ring 5 simultaneously so the second way also goes though a planetary gearbox and two stages o cylindrical stages 6 to 9. It should be noticed that the pinion 9 have the same rotation velocities n j [RPM]. On this condition there is developed the ratio o the planetary stage in (Bartelmus, Zimro 2010b). The possibility o condition evaluation or the planetary stage is given in (Bartelmus, Zimro 2009b). 2. OBJECT DESCRIPTION The considered object description is based on the paper (Wocka, 2003) and the scheme o the drive is give in igure 3. In the described system there is incorporated an overload mechanism. It is presumed that in normal operation the power is transmitted through a bevel stage (gears 1, 2 ) a cylindrical stage (gears 3, 4 ) a planetary stage (gears 5, 6, 7 ). The gear 5 is ixed during normal operation o the drive. It is ixed by the overload mechanism. The last stage o the system is a planetary (gears 8, 9, 10 ) stage with a ixed gear 10. During the overloading the power is transmitted to the overload mechanism. The power is transmitted through a bevel stage (gears 1, 2 ), a cylindrical stage (gears 3, 4 ), a second cylinder stage with a third wheel 6. It is presumed that the arm/carrier o a planetary gearbox (gears 5, 6, 7 ) is now ixed because the bucked wheel is stopped by overloading, 3. DEVELOPMENT OF CHARACTERISTIC FREQUENCIES The system presented in the igure 3 during normal operation works using a bevel stage gearbox with a ratio a cylindrical stage with ratio a planetary gearbox with ratio 2 u b =, (1) 1 u cy =, (2) 4 3 u p 1 = 1+, (3) 5 7

5 Fundamentals or condition monitoring and diagnostics or driving bucket wheel system 9 in this case the gear 5 is stopped by the brake which is adjusted to the constant moment M b [Nm]. The system also includes a planetary gearbox with a ratio u p = 1. (4) 8 The planetary gearboxes are complex gearboxes or, which principles or inding their ratios are given in a paper (Bartelmus, Zimro 2010b). Knowing the above relation one may treat the system as a compound gearbox with a total ratio = = ut ubucyu u 1 1. (5) Under condition o overloading the bucked wheel is stopped and the power is transmitted to the brake through a bevel stage gearbox with a ratio as given by (1) and a cylindrical stage as given by (2). In the case o overloading the and the bucket wheel is stoped and n j5 = 0 so the planetary gearbox is redused to the cylindrical stage with idle gear or third wheel 6 and the ratio o the omer planetary gear (gears 5, 6, 7 ) is now 5 u cy 2 = (6) 7 and transmited moment rom the electric motor equels to M b. Further the power is transmited by a planetary gearbox with (gears 11, 12, 13 ) which works as multiplicater with a ratio u p =. (7) And now one may treat the system as a compound gearbox with a total ratio o the gearbox rom the motor to the brake is The braking toque/moment is u = u u u u. (8) t b b cy t cy2 p3 M = u k M, (9) M m [Nm] the nominal/rated moment o the electric motor, k o coeicient o overloading k o 1. For the condition monitoring o the system there is a need ind meshing requencies. o m

6 10 W. BARTELMUS The meshing requences are given in notation as is given in article (Bartelmus, Zimro 2011) or example 12 means the requency or gears 1 and 2 and is evaluated rom the statment n =. (10) Where n 1 rotation valocity o an electric motor in RPM. Meshing requency or gears 3 and 4 is n23 34 =, (11) n 1 1 n 2 =. (11a) 2 A meshing requency or the planerary stage (gears 5, 6, 7 ) according to the developments given in (Bartelmus, Zimro 2010b) is in (12). The meshing requency is according to an above notation, and should be also noticed that in that planetary gearbox the gear 5 is ixed during normal operation. 56 n357 = 67 =, (12) 5 + 7) n n =. (13) Meshing requency or the planerary stage (gears 8, 9, 10 ) according to the developments given in (Bartelmus, Zimro, 2010b) 89 n j58 10 = 910 =, (14) ( + ) 8 10 n n j 5 = ( + 7 ). (15) 2 4 The output rotation velocity in RPM is given by the statment n n j 7 =. (16) + ) ( + ) (

7 Fundamentals or condition monitoring and diagnostics or driving bucket wheel system 11 The output rotation can be also given by (17) n 7 =. (17) 1 n j ut Rotation valocities or satalites 6 and 9 according to the depiction in igure 3 accoding to article (Bartelmus Zimro, 2011) are n 3 7 n 4 =, (18) 26 n 6 n j58 =. (19) 2 Next step or a gearbox ault identyication is connected with local aults. Local ault reqencies are given equivelently or gears 1, 2, 3 and 4 n1 n2 1 l = ; 2l 3l = = ; n3 4 l =, (20) 1l means a requency o a local ault or gear 1 and so on or the other gears. For the planetary stage (gear 5 ixed) with gears 5, 6, 7, according to (Bartelmus, Zimro 2011) n37s 4n357 n35s 5 l = ; 6 l = ; l =, (21) 5 + 7) 7 5 ) 5 + 5) s is a number o satalites in a planetary stage. For the planetary stage (gear 10 ixed) with gears 8, 9, 10, according to (Bartelmus, Zimro 2011) 8l n j510s = ; ( + ) l 4n j5810 = ; 2 2 ) l n j58s =, (22) ( + ) 8 10 s is a number o satalites in a planetary stage. Carrier requencies equivelently or the planetary stage with gears 5, 6, 7, and 8, 9, 10 Passing requencies n37 j = ; 5 + 7) n s Frequency o meeting the same teeth. j n j58 =. (23) ( + ) 8 10 j5 p 1 = 1 ; j7 2 2 n p = s. (24)

8 12 W. BARTELMUS Folowing the discusion given in (Bartelmus, Zimro 2011) and (Bartelmus 2006), here it is repeated. One may ask a question: ater how many rotations do the same teeth meet producing a similar excitation? I this number is denoted by N and multiplied by number o teeth 1, then it is the number o excitations ater which the excitation cycle will be repeated. Number N corresponds to the number o revolutions o the pinion ater which the same teeth will meet again. It is calculated rom ratio 1 / 2, e.g. 38/50, and ater the elimination o common divisors a ratio is 19/25, N = 25, is obtained. Thus the same teeth meet ater 25 revolutions o the pinion. The duration o one excitation is 1 τ 1 = =, [s] (25) n 1 1 a meshing generates a sequence o recurrent excitations with period N T p = τ 1N1 =, [s] (26) n a sequence o excitations orms a unction whose repetition rate is p 1 1 n1 = =, [H] (27) T N p Following the statements (25) to (27) one can evaluate the recurrent requencies or the bevel stage (gears 1, 2 ) and cylindrical stage (gears 3, 4 ). More attention should be given or planetary gear stages. Let start with a planetary stage with gears 5, 6, 7, the gear 6 is ixed during the normal operation. Following the statement (25) the duration o one excitation should be evaluated which in the case o the considered planetary stage with ixed 5 is given by the statement From (26) and (27) 1 + ) 5 7 τ 1 = =. (28) 56 n357 n =. (29) ) N In the statement (29) is given the recurrent requency or the gears 7, 6. Where N is evaluated rom ratio 7 / 6 ater elimination o common divisors the ratio goes to the orm m is a common divisor. 7 6 mm M = =, (30) mn N

9 Fundamentals or condition monitoring and diagnostics or driving bucket wheel system 13 Following the presented above procedures the recurrent requency or gears 6, 5 is n =, (31) ) 6N 6 5 mm M = =. (32) mn N The recurrent requency or gears 8, 9 or the planetary stage with gears 8, 9, 10 is 8 9 n =, (32) j ) N mm M = =. (33) mn N The recurrent requency or gears 8, 9 or the planetary stage with gears 8, 9, 10 is 10 n = (34) 9 j ) 9N mm M = =. (35) mn N As it was mansioned in the case o overloading the bucket wheel is stoped and n j5 = 0 so the planetary gearbox is redused to the cylindrical stage with idle gear or third wheel 6 and the ratio o the omer planetary gear (gears 5, 6, 7 ) is now is given by (6) and transmited moment rom the electric motor equels to M b. Further the power is transmited by a planetary gearbox with (gears 11, 12, 13 ) which works as multiplicater with a ratio (7). The meshing requencies or bevel and cylindrical gear as is given in (10) and (11). But urther consideration ought to based on that n j5 = 0. The bucked wheel is overloaded so the meshing requency or the cylindrical stage with the third wheel 6 is n37 76 = 65 =. (36)

10 14 W. BARTELMUS Meshing requency or a planetary stage with (gears 11, 12, 13 ) is n = 1213 =. (37) ) Frequency o local aults can be evaluated rom the ollowing statements n3 2n 7 l = ; 4 n j8 6 l = ; 5l =, (38) n 3 7 n 4 =. (39) 6 The local aults or a planetary stage with (gears 11, 12, 13 ) and gear 13 ixed) according to (Bartelmus, Zimro 2010b) n1013s 4n n1011s 11l = ; 12l = ; l =, (40) ) 13 11) ) s is a number o satalites in a planetary stage. The carrier requency is n10 n 11 j6 j = =. (41) ) The passing requency n j6 = s, (42) s is a number o satalites in a planetary stage. The recurrent requency or gears 11, 12 or the planetary stage with gears 11, 12, 13 is 12 n =, (43) ) N mm M = =. (44) mn N The recurrent requency or gears 12, 13 or the planetary stage with gears 11, 12, 13 is n =, (45) ) 12N

11 Fundamentals or condition monitoring and diagnostics or driving bucket wheel system mm M = =. (46) mn N 4. FINAL CONSIDERATION Gearbox is a system which may appear as a one stage gearbox or as a compound or complex gearbox. Most research on the gearbox damage process is done on the one stage gearbox. One stage gearbox system consists o gears, bearings and a case. Considering the damage process o the gearbox all the elements are treated separately by researchers. For example one may investigate the possibility o monitoring bearing aults making artiicial ault on one element o the bearing, an inner, outer ring or a ball. One may investigate on condition monitoring o a making artiicial breakage o a gear tooth. It as a wrong way o investigating on degradation process and possible condition monitoring or investigation and assessment o a gear ault. It is basic methodology error, because this investigation do not have too much in common with real degradation process. First o all one ought to treat the gearbox stage as a unity. For this unity it is a need to develop the measure o its condition. The measure should be made under deerent values o external loads. The measure o one stage gearbox condition appeared to be a linear unction o applied external load (Bartelmus, Zimro 2009b). This measure should evaluate ater gearbox run in. In the case o the compound or complex gearbox the measure o condition should evaluate or each stage o the gearbox treating the stage as a unity. That means separately or a cylindrical stage, bevel stage or worm stage i one is considering the compound gearbox. In the case o complex gearboxes which incorporates planetary gearboxes one should give more attention to division the system into subsystems and reduce the complex system into the compound system. An example o a complex gearbox system is given in igures 1 to 3. For each stage or subsystem there is a need to evaluate the measure o its condition. In the process o a gearbox condition change. 5. CONCLUSIONS In the paper is given consideration on developing the characteristic requencies which can be used or condition monitoring o the new design o the drive o a bucked wheel or a bucked wheel excavator with overloading mechanism. ACKNOWLEDGMENT This paper was inancially supported by Polish State Committee or Scientiic research as research project NN

12 16 W. BARTELMUS REFERENCES BARTELMUS W., ZIMROZ.R., 2007, Metoda diagnostyki prekładni planetarnej, Górnictwo i geologia IX (Red. nauk. Walter Bartelmus), Wrocław, Oicyna Wydawnica PWr., BARTELMUS W., ZIMROZ R., 2009a, Vibration condition monitoring o planetary gearbox under varying external load, Mechanical Systems and Signal Processing, 23, BARTELMUS W., ZIMROZ R., 2009b, A new eature or monitoring the condition o gearboxes in nonstationary operation conditions, Mechanical Systems and Signal Processing, 23, BARTELMUS W., CHAARI F., ZIMROZ R., HADDAR M., 2010, Modelling o gearbox dynamics under time varying non-stationary operation or distributed ault detection and diagnosis, European Journal o Mechanics A/Solids, 29, BARTELMUS W., ZIMROZ R., 2008, Problems and solutions in condition monitoring and diagnostics o open cast monster machinery driving systems, Diagnostyka, 3/47, 55. BARTELMUS W., 2009, Statistical eature estimation o the process describing object condition change or maintenance decision, Prace Naukowe Instytutu Górnictwa Politechniki Wrocławskiej, Górnictwo i geologia XII, Wrocław. BARTELMUS W., ZIMROZ R., 2010a, Way o non-stationary signal analysis generated by machinery or eature extraction and their processing, International Congress on Noise Control Engineering, June 13 16, Lisbon, Portugal. BARTELMUS W., ZIMROZ R., 2010b, Heavy machinery diagnostics and condition monitoring, Proceedings o International Conerence on Condition Monitoring and Machine Failure Prevention Technology, June 22 24, Stratord upon Avon, England. BARTELMUS W., ZIMROZ R., 2011, Vibration spectra characteristic requencies or condition monitoring o mining machinery compound and complex gearboxes, Górnictwo i Geologia, Scientiic Papers o the Institute o Mining. BARTELMUS W., 2006, Condition monitoring o open cast mining machinery, Oicyna Wydawnica Politechniki Wrocławskiej, Wrocław. WOCKA N., Rola i nacenie spręgła preciążeniowego, Węgiel Brunatny, nr 4 (45), PODSTAWY MONITOROWANIA I DIAGNOSTYKI UKŁADU NAPĘDOWEGO Z MECHANIZMEM PRZECIĄŻENIOWYM KOŁA CZERPAKOWEGO KOPARKI KOŁOWEJ Praca predstawia podstawy monitorowania I diagnostyki stanu układu napędowego koła cerpakowego, który ostał skonstruowany do eksploatacji łóż o więksonych oporach urabiania. Podstawy predstawiają cęstotliwości charakterystycne aębienia, cęstotliwości uskodeń lokalnych, cęstotliwości obrotów jarma itp.