Investigating Efficiency of a Five-Mass Electromechanical System having Damping Friction, Elastic Coupling and Clearance

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1 Invetigating Efficiency of a Five-Ma Electromechanical Sytem having Damping Friction Elatic oupling and learance Mr. Aboah Boateng Emmanuel Student (BSc. Electrical and Electronic Engineering Department Univerity of Mine and echnology arkwa hana. Mr. Normanyo Erwin Senior Lecturer Electrical and Electronic Engineering Department Univerity of Mine and echnology arkwa hana. Abtract Electromechanical ytem ued in indutrial etup have ome drawback in their operation which have been a major challenge of reearcher over the year in their deign. Notable among thee drawback are damping friction elatic coupling and clearance. Recent work in the literature however are limited to one-ma two-ma and on a few occaion threema ytem model in the quet to invetigate the effect of thee drawback. hi work eek to extend and improve upon the quality of the exiting model by formulating a model of a fivema ytem having thee drawback for the purpoe of efficiency invetigation. In thi reearch a mathematical model and ubequently MALAB Simulink model of a generic five-ma ytem wa developed for imulation. Simulation reult revealed that in the analyi of the efficiency of a five-ma ytem the effect of damping friction i paramount a compared to that of elatic coupling and clearance. Keyword Five-ma ytem electric drive clearance tiffne I. INRODUION In everal indutrial etup uch a teel rolling mill flexible robot arm large pace tructure machine tool helicopter control ytem lurry pumping ytem meaurement machine and ball mill drive are motly conidered a two-ma or multi-ma ytem. Electromechanical ytem ued in thee indutrial etup conit of electrical and mechanical part. Mechanical element ued in preciion poitioning ytem and power tranfer uch a gear and clutche poe limitation like damping friction elatic coupling and clearance which affect the efficient and effective operation of electromechanical ytem []. Sytem with infinite tiffne and without clearance are qualified a one-ma ytem and are quite well analyed. omplex ytem with more than one ma coupling between the driving ource and connected load are known a multima ytem. Motly the implification a a one-ma ytem i not appropriate and lead to unatifactory control performance []. Moreover in order to minimie noie and improve the efficiency of electromechanical ytem it i eential to accurately predict the dynamic behaviour of thee ytem hence the need for a multi-ma ytem modelling. Ocillation and intabilitie in drive ytem a a reult of clearance finite tiffne and friction affect the efficient tranfer of power from prime mover to the connected load []. Energy cot have ignificantly increaed and environmental awarene ha arien recently. hi i one of the main reaon why energy effectivene ha become an important matter in deigning indutrial drive. he main goal of thi reearch therefore i to invetigate the efficient utiliation of electric power of a five-ma ytem having damping friction elatic coupling and clearance. II. RELAED WORKS A ma ytem i baically a drive chain that conit of a driving machine (prime mover coupling element (coupling gear etc. and a driven machine (power conumer []. he nature of the coupling between the prime mover and the mechanical element or load claifie them a either ingle or multi-ma ytem. One-ma ytem erve a bai for modelling electromechanical ytem but are not popular due to their limitation and deviation from reality [] []. woma ytem are very popular and well analyed due to their implicity and eay modelling with little deviation from reality. hree-ma ytem model have few literature related to them though they prove to be better and cloer to reality a compared to a two-ma ytem [6]. Work on five-ma ytem however are non-exitent in the literature. Sytem uch a helicopter control mechanim and ball mill drive are ome example of five-ma ytem. herefore lack of relevant literature on five-ma ytem model call for further reearch to extend and improve upon the quality of the exiting model of two-ma and three-ma ytem. III. MEHODS USED Five-ma ytem are complex electromechanical ytem having elatic coupling and connection between five mae with the firt ma uually the prime mover tranferring mechanical energy to a load (final ma through variou mechanical element. he mechanical coupling between thee mae may affect the efficient tranfer of energy to the final ma due to elatic coupling clearance damping friction etc. which are inevitable in the deign of indutrial drive []. A. Schematic Diagram of a Five-ma Sytem A chematic diagram of a five-ma ytem having elatic coupling clearance and damping friction i hown in Fig.. 9

2 r J r r r J J J J b b r Fig. A Schematic Diagram of a Five-Ma Sytem having Damping Friction Elatic oupling and learance he five-ma electromechanical ytem conidered in Fig.. ha moment of inertia J and J repreenting inertia of the electric prime mover driving the ytem and the final load repectively. Moment of inertia J J and J repreent the mae of different mechanical element uch a gear haft clutche etc. that aid in the actuator mechanim. he coupling between the mae are conidered to be elatic repreented by and which characterie the tiffne between mae and and and and and repectively. he peed of rotation and of electric prime mover and the load repectively are different. hi i partly due to the elatic coupling and kinematic clearance and between mae and and and and and repectively. he damping coefficient of the prime mover and the load are denoted by and repectively. B. Mathematical Model of the Five-ma Sytem Baed on Newton law of rotational motion the mathematical model of the Five-ma ytem wa derived conidering the variou direction of motion of the mae in Fig.. he mathematical model wa tranformed into the Laplace domain for imulation. Baed on Fig. the tranfer function of mae and were derived a follow: r J b ( b ( J r J ( r J ( r r b ( J b ranfer function repreenting rotational tiffne between mae and and and and and were alo derived a follow: Y (6 ( b b Y (7 ( Y (8 ( Y (9 ( he correponding tranfer function were ued to develop a block diagram of the five-ma electromechanical ytem for efficiency invetigation a hown in Fig.. r Y J Y Y J J J b Jb r r r r Y Fig. Block Diagram of the Ball Mill Drive a a Five-Ma Electromechanical Sytem having Damping Friction Elatic oupling and learance. Simulation Fig. repreent a MALAB Simulink model of the fivema ytem having damping friction elatic coupling and clearance. he model wa deigned in uch a way to produce a correponding output power and efficiency of the ytem a the input parameter change. he clearance in the model of Fig. i expreed by the dead zone block of Simulink. A number of cenario were conidered in the imulation of the five-ma ytem model. he cenario conidered are a follow:. Varying damping coefficient at contant tiffne and clearance parameter.. Varying tiffne value at contant damping and clearance parameter.. Varying clearance parameter at contant tiffne and damping friction. 9

3 Efficiency (% Power onumption (W Fig. Simulink Model of the Five-ma Sytem having Damping Friction Elatic oupling and learance he clearance in the model of Fig. i expreed by the dead zone block of Simulink which pecifie the upper and lower limit of the torional angle at the joint. Only electromagnetic tranient are expected in the ytem before the dead zone i paed and afterward the next ma tart to exert influence on the dynamic of the ytem []. It i convenient to invetigate dynamic characteritic of the five-ma ytem in Simulink becaue it provide the poibility to conider non-linearity of any type. able how the preferred tandard parameter ued for the imulation of the five-ma ytem model. hee parameter were varied in variou cenario to identify the influence of damping friction elatic coupling and clearance on the efficiency of the ytem. A. Simulation Reult he reult of input and output power a well a efficiencie of imulation of the generic five-ma ytem model are preented in Fig. to Fig. 7. With the exception of Fig. 7 the firt three graph of Fig. and 6 are related to power conumption wherea their lat graph (fourth are related to efficiency of the ytem. a b = b = 0 in Nm/rad/ P = 6 W P 0 = 66. W able : Standard Parameter of Simulation Parameter Value Unit Step Input orque 00 Nm Stiffne oefficient 0000 Nm/rad Stiffne oefficient Nm/rad Stiffne oefficient 000 Nm/rad Stiffne oefficient 000 Nm/rad learance mm learance learance 8 mm mm learance 8 mm Damping Friction of Motor (b Nm/rad/ Damping Friction of Load (b 0 Nm/rad/ b c b = 80 b = 00 in Nm/rad/ b = b = 60 in Nm/rad/ P = 6 W P = 6 W P 0 = 66. W P 0 = 089. W IV. RESULS AND DISUSSIONS he reult of the imulation of the variou cenario are preented and dicued in thi ection. he central point of dicuion of the reult i the influence of damping friction elatic coupling and clearance on electric power utiliation and tability of the five-ma ytem. d η a.% η b.07% η c 86.% ime Fig. Varying Damping oefficient at ontant Stiffne and learance 96

4 Efficiency (% Power onumption (% a P = 6 W P 0 = 089. W Power onumption (W Efficiency (% = 0000 = = 000 = 000 in Nm/rad b c ime P = 6 W P = 6 W P 0 = 090 W P 0 = 088 W Efficiency η a 86.% η b 86.% η c 86.0% d 0% increae of and 0% decreae of and Fig. Varying Stiffne Value at ontant Damping and learance Parameter a b c d ime P = 6 W 8 8 in mm Efficiency 00% increae of 80% decreae of P = 6 W P = 6 W Δ Δ P 0 = 089. W P 0 = 088. W P 0 = W η a 86.% η b 86.0% η c 86.08% Fig. 6 Varying learance Value at ontant Stiffne and Damping oefficient Power onumption (W ime J = 0 kgm J = 0 kgm J = kgm J = kgm P 0 = 89 W at J = 0 kgm P 0 = 9 W at J = 0 kgm P 0 = W at J = kgm P 0 = 0 W at J = kgm Fig. 7 Varying Ma (Load at ontant Stiffne Damping Friction and learance oefficient B Dicuion of Simulation Reult he imulation reult of Fig. howed that damping friction had the greatet influence on the efficiency of the generic five-ma ytem model. For an input power of 6 W relatively high damping coefficient of b = 80 Nm/rad/ and b = 00 Nm/rad/ reulted in a very low output power of 66. W with a correponding poor efficiency of.07%. hi wa due to the fact that the ytem wa overdamped and hence a higher percentage of the input energy wa converted to heat reulting in higher loe. At relatively low damping coefficient of b = Nm/rad/ and b = 0 Nm/rad/ for the ame input power a low output power of 66. W wa recorded for an efficiency of.%. hi wa a a reult of the ytem being underdamped hence there wa a high level of intability and ocillation in the ytem which affected the efficient operation of the ytem. However at moderate damping coefficient of b = Nm/rad/ and b = 60 Nm/rad/ there wa an increae in output power to 089. W giving an efficiency of 86.%. hi wa due to the tolerable damping friction during the tranient period for only 0.. From Fig. tiffne value of the elatic coupling had le effect on efficiency of the five-ma ytem but they rather affected the tability of the ytem. From Fig.. at 0% decreae in the preferred tiffne value the output power decreaed lightly to 088 W giving an efficiency of 86.0%. However there wa poor tability of the ytem due to higher frequency of ocillation during the tranient period. Moreover 0% increae in the preferred tiffne value reulted in a little increae in the output power to 090 W offering an efficiency of 86.% and a higher tability which wa attributed to lower amplitude of ocillation for a le ettling time of 0.. Finally reult of the preferred tiffne value of = 0000 Nm/rad = Nm/rad = 97

5 000 Nm/rad and = 000 Nm/rad produced an output value of 089. W reulting in an efficiency of 86.% with high ytem tability. From Fig. 6 the reult of varying clearance value howed that clearance had no meaningful effect on efficiency of the generic five-ma ytem. At tandard clearance value of and the output power tood at 089. W giving an efficiency of 86.%. However for 00% increae and 80% decreae in the tandard clearance value the output power wa 088. W and W repectively which reulted in efficiencie of 86.0% and 86.08% repectively. With no ignificant influence of clearance on the ytem efficiency it buttreed the point that clearance in ma ytem caue the load haft peed to lag behind the motor haft peed during tranient period but once teady tate i achieved they ettle at the normal operating peed reulting in normal output power []. Higher load inertia reulted in higher power conumption with le tability and vice vera a hown in Fig. 7. At load inertia of 0 kgm the power conumption wa relatively high at 89 W with le tability. hi wa becaue at higher moment of inertia more kinetic energy i required to caue rotation of the load and vice. Hence load inertia of 0 kgm kgm and kgm reulted in decreaing rate of power conumption of 9 W W and 0 W repectively. It wa poited by [] that increaing value of load inertia reult in increaing tranient period of peed and torque. hi explain why the ettling time and overhoot of power conumption waveform of Fig. 7 increaed with increaing load inertia ince power i a product of peed and torque. REFERENES [] F.Y.M. Mohd Q. Abdul and B.A. Aminudin B. A omparative Study on ontrol Method for wo-ma Sytem International Journal on Advanced Science Engineering and Information echnology Vol. pp [] S. Juraiti R. Rinkeviciene and A. Kilikeviciu wo-ma Variable Speed Drive Electronic and Electrical Engineering Journal Vol. 0 No. pp [] K. Drozdz Adaptive ontrol of the Drive Sytem with Elatic oupling uing Fuzzy Kalman Filter with Dynamic Adaptation of Selected coefficient Maintenance and Reliability Vol. 7 No. pp [] S. Juraiti Reearch of ranient Proce in Electromechanical woma Sytem Unpublihed Summary of Doctoral Diertation Vilniu edimina echnical Univerity Lithu ania pp 0. [] S. hazanfar Modelling and Simulation of a wo-ma Reonant Sytem with Speed ontroller International Journal of Information and Electronic Engineering Vol. No. pp [6] M. Kobuch S. Eichtadt L. Klau and. Brun (0 Invetigation for the Model-baed Dynamic alibration of Force randucer by uing Shock Force rd International onference ape own South Africa pp V. ONLUSIONS Baed on the finding of the generic five-ma ytem model it can be concluded that:. Very low and very high damping coefficient reult in poor efficiency whilt moderate damping coefficient give efficiencie more than 8%.. hange in tandard tiffne value to the tune of hardly affect the efficiencie which tand high at value of at leat 86%. It rather affect the tabilty of the five-ma ytem. hu the lower the tiffne value the le table the ytem.. hange in tandard clearance value from 80% to 00% of the preferred value reult in no meaningful change in efficiency that tand at above 86%.. he more the load inertia the higher goe the power conumption and more untable the five-ma mechanical ytem become. 98