Investigating Efficiency Of A Five-Mass Electromechanical . - IJERT
Published by : http://www.ijert.org International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 6 Issue 06, June - 2017 Investigating Efficiency of a Five-Mass Electromechanical System having Damping Friction, Elastic Coupling and Clearance Mr. Aboah Boateng Emmanuel, Student (BSc.), Electrical and Electronic Engineering Department, University of Mines and Technology, Tarkwa, Ghana. Abstract— Electromechanical systems used in industrial setups have some drawbacks in their operation which have been a major challenge of researchers over the years in their design. Notable among these drawbacks are damping friction, elastic coupling and clearance. Recent works in the literature however are limited to one-mass, two-mass and on a few occasions, threemass system models in the quest to investigate the effects of these drawbacks. This work seeks to extend and improve upon the quality of the existing models by formulating a model of a fivemass system having these drawbacks for the purpose of efficiency investigation. In this research, a mathematical model and subsequently, MATLAB Simulink model of a generic five-mass system was developed for simulations. Simulation results revealed that in the analysis of the efficiency of a five-mass system, the effect of damping friction is paramount as compared to that of elastic coupling and clearance. Keywords— Five-mass system, electric drive, clearance, stiffness I. INTRODUCTION In several industrial setups such as steel rolling mills, flexible robot arms, large space structures, machine tools, helicopter control system, slurry pumping system, measurement machines and ball mill drives are mostly considered as two-mass or multi-mass systems. Electromechanical systems used in these industrial setups consist of electrical and mechanical parts. Mechanical elements used in precision positioning systems and power transfer such as gears and clutches pose limitations like damping friction, elastic coupling and clearances which affect the efficient and effective operation of electromechanical systems [1]. Mr. Normanyo Erwin, Senior Lecturer, Electrical and Electronic Engineering Department, University of Mines and Technology, Tarkwa, Ghana. awareness has arisen recently. This is one of the main reasons why energy effectiveness has become an important matter in designing industrial drives. The main goal of this research therefore, is to investigate the efficient utilisation of electric power of a five-mass system having damping friction, elastic coupling and clearance. II. RELATED WORKS A mass system is basically a drive chain that consists of a driving machine (prime mover), coupling elements (couplings, gears etc.) and a driven machine (power consumer) [4]. The nature of the couplings between the prime mover and the mechanical elements or load classifies them as either single or multi-mass systems. One-mass systems serve as basis for modelling electromechanical systems but are not popular due to their limitations and deviations from reality [5], [4]. Twomass systems are very popular and well analysed due to their simplicity and easy modelling with little deviation from reality. Three-mass system models have few literature related to them, though they prove to be better and closer to reality as compared to a two-mass system [6]. Works on five-mass systems however, are non-existent in the literature. Systems such as helicopter control mechanism and ball mill drives are some examples of five-mass systems. Therefore, lack of relevant literature on five-mass system models calls for further research to extend and improve upon the quality of the existing models of two-mass and three-mass systems. III. METHODS USED Systems with infinite stiffness and without clearance are qualified as one-mass systems and are quite well analysed. Complex systems with more than one mass coupling between the driving source and connected loads are known as multimass systems. Mostly, the simplification as a one-mass system is not appropriate and leads to unsatisfactory control performances [2]. Moreover, in order to minimise noise and improve the efficiency of electromechanical systems, it is essential to accurately predict the dynamic behaviour of these systems, hence the need for a multi-mass system modelling. Five-mass systems are complex electromechanical systems having elastic couplings and connections between five masses with the first mass usually the prime mover transferring mechanical energy to a load (final mass) through various mechanical elements. The mechanical couplings between these masses may affect the efficient transfer of energy to the final mass due to elastic coupling, clearance, damping friction etc., which are inevitable in the design of industrial drives [1]. Oscillations and instabilities in drive systems as a result of clearance, finite stiffness and friction affect the efficient transfer of power from prime mover to the connected load [3]. Energy costs have significantly increased and environmental A. Schematic Diagram of a Five-mass System A schematic diagram of a five-mass system having elastic coupling, clearance and damping friction is shown in Fig. 1. IJERTV6IS060064 www.ijert.org (This work is licensed under a Creative Commons Attribution 4.0 International License.) 94
Published by : http://www.ijert.org Tr1 , T12 C12 International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 6 Issue 06, June - 2017 Δ 12 Tr2 , T23 C 23 Δ 23 Tr3 , T34 C 34 b1 T12 , ω T, ω1 2 Δ 45 C45 J3 J2 J1 Tr4 ,T45 Δ 34 Tr5 J4 J5 b5 T34 , ω 4 T23 , ω 3 T45 , ω 5 Fig. 1 A Schematic Diagram of a Five-Mass System having Damping Friction, Elastic Coupling and Clearance The five-mass electromechanical system considered in Fig. 3.1 has moment of inertia, J1 and J5 representing inertia of the electric prime mover driving the system and the final load respectively. Moment of inertia J2, J3, and J4 represent the masses of different mechanical elements such as gears, shafts, clutches etc. that aid in the actuator mechanism. The couplings between the masses are considered to be elastic, represented by C12, C23, C34 and C45 which characterise the stiffness between masses 1 and 2, 2 and 3, 3 and 4, and 4 and 5 respectively. The speed of rotation, ω1 and ω 5 of electric prime mover and the load respectively are different. This is partly due to the elastic couplings and kinematic clearances 12 , 23 , 34 and 45 between masses 1 and 2, 2 and 3, 3 and 4, and 4 and 5 respectively. The damping coefficients of the prime mover and the load are denoted by b1 and b 5 respectively. B. Mathematical Model of the Five-mass System Based on Newton’s law of rotational motion, the mathematical model of the Five-mass system was derived considering the various directions of motion of the masses in Fig. 1. The mathematical model was transformed into the Laplace domain for simulations. Based on Fig. 1, the transfer functions of masses 1, 2, 3, 4 and 5 were derived as follows: ω1 1 G1 (s) T Tr1 T12 b1ω 2 J1s b1 ω2 1 G 2 (s) T12 Tr2 T23 J 2 s ω3 1 G 3 (s) T23 Tr3 T34 J 3s ω4 1 G 4 (s) T34 Tr4 T45 J 4 s ω5 1 G 5 (s) T45 Tr5 b 5 ω5 J 5 s b 5 (1) (2) (3) (4) (5) Transfer functions representing rotational stiffness between masses 1 and 2, 2 and 3, 3 and 4, and 4 and 5 were also derived as follows: C12 T12 Y12 s (ω1 ω 2 ) IJERTV6IS060064 (6) C 23 T23 Y23 s (ω 2 ω 3 ) (7) C 34 T34 Y34 s (ω 3 ω 4 ) (8) C 45 T45 Y45 s (ω 4 ω 5 ) (9) The corresponding transfer functions were used to develop a block diagram of the five-mass electromechanical system for efficiency investigations as shown in Fig. 2. T23 T12 T34 T45 G1(s) Y12 (s) G2 (s) Y23 (s) G3(s) Y34 (s) G4 (s) Y45 (s) G5 (s) 1 1 1 C23 C12 T J1s b1 s J 2 s s J 3 s ω2 Tr1 ω5 ω4 ω3 Tr2 1 ω5 1 C34 C45 s J 4 s s J5s b5 Tr3 Tr4 Tr5 Fig. 2 Block Diagram of the Ball Mill Drive as a Five-Mass Electromechanical System having Damping Friction, Elastic Coupling and Clearance C. Simulations Fig. 3 represents a MATLAB Simulink model of the fivemass system having damping friction, elastic coupling and clearance. The model was designed in such a way to produce a corresponding output power and efficiency of the system as the input parameters changes. The clearance in the model of Fig. 3 is expressed by the dead zone block of Simulink. A number of scenarios were considered in the simulations of the five-mass system model. The scenarios considered are as follows: 1. Varying damping coefficients at constant stiffness and clearance parameters. 2. Varying stiffness values at constant damping and clearance parameters. 3. Varying clearance parameters at constant stiffness and damping friction. www.ijert.org (This work is licensed under a Creative Commons Attribution 4.0 International License.) 95
Published by : http://www.ijert.org International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 6 Issue 06, June - 2017 Fig. 3 Simulink Model of the Five-mass System having Damping Friction, Elastic Coupling and Clearance Table 1 shows the preferred standard parameters used for the simulation of the five-mass system model. These parameters were varied in various scenarios to identify the influence of damping friction, elastic coupling and clearance on the efficiency of the system. Table 1: Standard Parameters of Simulations Parameter Value Step Input Torque, T 100 Stiffness Coefficient, C12 50,000 Stiffness Coefficient, C23 60,000 Stiffness Coefficient, C34 3,000 Stiffness Coefficient, C45 3,000 Clearance, 12 5 Clearance, 23 8 Clearance, 34 Clearance, 45 Damping Friction of Motor (b1) Damping Friction of Load (b5) IV. Unit Nm Nm/rad Nm/rad Nm/rad Nm/rad mm mm 5 mm 8 3 10 mm Nm/rad/s Nm/rad/s RESULTS AND DISCUSSIONS The result of the simulations of the various scenarios are presented and discussed in this section. The central point of discussions of the results is the influence of damping friction, elastic coupling and clearance on electric power utilisation and stability of the five-mass system. IJERTV6IS060064 With the exception of Fig. 7, the first three graphs of Fig. 4, 5 and 6 are related to power consumption whereas their last graphs (fourth) are related to efficiency of the system. Powe r Consumption (W) It is convenient to investigate dynamic characteristics of the five-mass system in Simulink because it provides the possibility to consider non-linearity of any type. A. Simulation Results The results of input and output power as well as efficiencies of simulations of the generic five-mass system model are presented in Fig. 4 to Fig. 7. Efficie ncy (%) The clearance in the model of Fig. 3 is expressed by the dead zone block of Simulink which specifies the upper and lower limits of the torsional angle at the joints. Only electromagnetic transients are expected in the system before the dead zone is passed and afterwards the next mass starts to exert influence on the dynamics of the system [4]. a) b1 3, b5 10, in Nm/rad/s P1 1264 W P0 664.3 W b) b1 80, b5 100, in Nm/rad/s P1 1264 W P0 646.5 W c) b1 3, b5 60, in Nm/rad/s P1 1264 W P0 1089.3 W d) ηa 52.54% ηb 51.07% ηc 86.11% Time (s) Fig. 4 Varying Damping Coefficients at Constant Stiffness and Clearance www.ijert.org (This work is licensed under a Creative Commons Attribution 4.0 International License.) 96
Published by : http://www.ijert.org International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 6 Issue 06, June - 2017 P1 1265 W a) P0 1089.3 W J5 20 kgm2 P1 1265 W P0 1090 W 50% increase of C12, C23, C34 and C45 b) Power Consumption (W) Power Consumption (W) C12 50000, C23 60000, C34 3000, C45 3000, in Nm/rad J5 10 kgm2 J5 5 kgm2 J5 1 kgm2 P0 1894 W at J5 20 kgm2 50% decrease of C12, C23, C34 and C45 P1 1265 W Efficiency (%) c) ηa 86.11% Efficiency P0 1539 W at J5 10 kgm2 P0 1088 W ηb 86.13% P0 1241 W at J5 5 kgm2 P0 1130 W at J5 1 kgm2 ηc 86.03% Time (s) d) Fig. 7 Varying Mass 5 (Load) at Constant Stiffness, Damping Friction and Clearance Coefficients Time (s) Fig. 5 Varying Stiffness Values at Constant Damping and Clearance Parameter Powe r Consumption (%) P1 1265 W a) Δ 12 5, Δ 23 8, Δ 34 5, Δ 45 8, in mm 100% increase of Δ 12 , Δ 23 , Δ 34 , Δ 45 P1 1265 W b) P0 1088.5 W 80% decrease of Δ 12 , Δ 23 , Δ 34 , Δ 45 P1 1265 W c) Efficie ncy (%) P0 1089.3 W Efficiency P0 1088.9 W ηa 86.11%, ηb 86.05%, ηc 86.08% d) Time (s) Fig. 6 Varying Clearance Values at Constant Stiffness and Damping Coefficients IJERTV6IS060064 B) Discussions of Simulation Results The simulation results of Fig. 4 showed that damping friction had the greatest influence on the efficiency of the generic five-mass system model. For an input power of 1264 W, relatively high damping coefficients of b 1 80 Nm/rad/s and b5 100 Nm/rad/s resulted in a very low output power of 646.5 W with a corresponding poor efficiency of 51.07%. This was due to the fact that the system was overdamped and hence a higher percentage of the input energy was converted to heat, resulting in higher losses. At relatively low damping coefficients of b1 3 Nm/rad/s and b5 10 Nm/rad/s for the same input power, a low output power of 664.3 W was recorded for an efficiency of 52.54%. This was as a result of the system being underdamped, hence there was a high level of instability and oscillations in the system which affected the efficient operation of the system. However, at moderate damping coefficients of b1 3 Nm/rad/s and b5 60 Nm/rad/s, there was an increase in output power to 1089.3 W giving an efficiency of 86.11%. This was due to the tolerable damping friction during the transient period for only 0.3 s. From Fig. 5, stiffness values of the elastic couplings had less effect on efficiency of the five-mass system but they rather affected the stability of the system. From Fig. 4.2, at 50% decrease in the preferred stiffness values, the output power decreased slightly to 1088 W giving an efficiency of 86.03%. However, there was poor stability of the system due to higher frequency of oscillations during the transient period. Moreover, 50% increase in the preferred stiffness values resulted in a little increase in the output power to 1090 W offering an efficiency of 86.13% and a higher stability, which was attributed to lower amplitudes of oscillations for a less settling time of 0.3 s. Finally, results of the preferred stiffness values of C12 50000 Nm/rad, C23 60000 Nm/rad, C34 www.ijert.org (This work is licensed under a Creative Commons Attribution 4.0 International License.) 97
Published by : http://www.ijert.org International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 6 Issue 06, June - 2017 3000 Nm/rad and C45 3000 Nm/rad produced an output value of 1089.3 W resulting in an efficiency of 86.11% with high system stability. From Fig. 6, the results of varying clearance values showed that clearance had no meaningful effect on efficiency of the generic five-mass system. At standard clearance values of and the output power stood at 1089.3 W giving an efficiency of 86.11%. However, for 100% increase and 80% decrease in the standard clearance values, the output power was 1088.5 W and 1088.9 W respectively which resulted in efficiencies of 86.05% and 86.08% respectively. With no significant influence of clearance on the system’s efficiency, it buttressed the point that clearance in mass systems cause the load shaft speed to lag behind the motor shaft speed during transient periods but once steady state is achieved, they settle at the normal operating speeds resulting in normal output power [4]. Higher load inertia resulted in higher power consumption with less stability and vice versa as shown in Fig. 7. At load inertia of 20 kgm2, the power consumption was relatively high at 1894 W with less stability. This was because at higher moment of inertia, more kinetic energy is required to cause rotation of the load and vice. Hence, load inertia of 10 kgm2, 5 kgm2, and 1 kgm2 resulted in decreasing rate of power consumption of 1539 W, 1214 W and 1130 W respectively. It was posited by [3] that increasing values of load inertia result in increasing transient periods of speed and torque. This explains why the settling times and overshoots of power consumption waveforms of Fig. 7 increased with increasing load inertia since power is a product of speed and torque. V. REFERENCES [1] [2] [3] [4] [5] [6] F.Y.M. Mohd, Q. Abdul, and B.A. Aminudin, B. A, “Comparative Study on Control Method for Two-mass Systems”, International Journal on Advanced Science Engineering and Information Technology, Vol. 2, pp. 63 – 67, 2012. S. Juraitis, R. Rinkeviciene, and A. Kilikevicius, “Two-mass Variable Speed Drive”, Electronics and Electrical Engineering Journal, Vol. 30, No. 4, pp. 25 – 28, 2010. K. Drozdz, “Adaptive Control of the Drive System with Elastic Coupling using Fuzzy Kalman Filter with Dynamic Adaptation of Selected coefficients”, Maintenance and Reliability, Vol. 17, No. 4, pp. 561 – 568, 2015. S. Juraitis, “Research of Transient Process in Electromechanical Twomass System”, Unpublished Summary of Doctoral Dissertation, Vilnius Gediminas Technical University, Lithu ania, 24pp, 2013. S. Ghazanfar, “Modelling and Simulation of a Two-mass Resonant System with Speed Controller”, International Journal of Information and Electronics Engineering, Vol. 3, No. 5, pp. 449 – 452, 2013. M. Kobusch, S. Eichstadt, L. Klaus, and T. Bruns, (2014), “Investigations for the Model-based Dynamic Calibration of Force Transducers by using Shock Forces”, 3rd TC22 International Conference, Cape Town, South Africa, pp. 127 – 135, 2014. CONCLUSIONS Based on the findings of the generic five-mass system model, it can be concluded that: 1. Very low and very high damping coefficients result in poor efficiency whilst moderate damping coefficients give efficiencies more than 85%. 2. Changes in standard stiffness values to the tune of hardly affect the efficiencies which stand high at values of at least 86%. It rather affects the stabilty of the five-mass system. Thus, the lower the stiffness value, the less stable the system. 3. Changes in standard clearance values from 80% to 100% of the preferred values result in no meaningful change in efficiency that stands at above 86%. 4. The more the load inertia, the higher goes the power consumption and more unstable the five-mass mechanical system becomes. IJERTV6IS060064 www.ijert.org (This work is licensed under a Creative Commons Attribution 4.0 International License.) 98
driving machine (prime mover), coupling elements (couplings, gears etc.) and a driven machine (power consumer) [4]. The nature of the couplings between the prime mover and the multi -mass systems. One mass systems serve as basis for modelling electromechanical systems but are not popular due
The Five Senses: Smell Smell Science: The Nose Knows! Your Sense of Taste The Five Senses: Taste Taste Test A Tasty Experiment Your Sense of Touch Your Sense of Touch: Cold Five Senses Your Five Senses #2 Learning the Five Senses My Five Senses Match Your Five Senses #1 Match Your Five Senses #2 Match Your Fiv
approach to character creation that is the foundation of Five by Five. The 5x5 task roll is original to Five by Five, but combat, weapons, and armor were all adapted from Warhammer Fantasy Roleplay.2 Five by Five was created ad-hoc for playing a quick game session with some friends by m
akuntansi musyarakah (sak no 106) Ayat tentang Musyarakah (Q.S. 39; 29) لًََّز ãَ åِاَ óِ îَخظَْ ó Þَْ ë Þٍجُزَِ ß ا äًَّ àَط لًَّجُرَ íَ åَ îظُِ Ûاَش
Collectively make tawbah to Allāh S so that you may acquire falāḥ [of this world and the Hereafter]. (24:31) The one who repents also becomes the beloved of Allāh S, Âَْ Èِﺑاﻮَّﺘﻟاَّﺐُّ ßُِ çﻪَّٰﻠﻟانَّاِ Verily, Allāh S loves those who are most repenting. (2:22
Chapter 3: Research design and methods for investigating the factors affecting teachers’ use of ICT (Phase 1) Page 63 Chapter 3 Research design and methods for investigating the factors affecting teachers’ use of ICT (Phase 1) The first section of this chapter deals with general design issues for the study as a whole.
Lesson Title: Investigating Special Quadrilaterals Lesson duration: 60-80 minutes Stage: 2 Year: 3 Rationale: By investigating the properties of special quadrilaterals, children build a deep understanding of what they are, and learn to identify and describe them when presented in different sizes and orientations. To ensure students d
Polynomial Functions Investigating Graphs of Polynomial Functions Holt Algebra 2 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 2. Holt McDougal Algebra 2 Investigating Graphs of Polynomial Functions Warm Up Identify all the real ro
Common Core State Standards for Mathematics and Contexts for Learning Mathematics byCatherine Twomey Fosnot andColleagues from Mathematics in the City and the Freudenthal Institute Investigating Number Sense, Addition, and Subtraction GRADES K-3 Investigating Multiplication and Division GRADES 3-5 Investigating Fractions, Decimals, and Percents GRADES 4-6
