 Open Access
 Total Downloads : 243
 Authors : Mr. Aboah Boateng Emmanuel, Mr. Erwin Normanyo
 Paper ID : IJERTV6IS060064
 Volume & Issue : Volume 06, Issue 06 (June 2017)
 Published (First Online): 03062017
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Investigating Efficiency of a FiveMass 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.
Mr. Normanyo Erwin,
Senior Lecturer,
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 onemass, twomass and on a few occasions, three mass 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 five mass system having these drawbacks for the purpose of efficiency investigation. In this research, a mathematical model and subsequently, MATLAB Simulink model of a generic fivemass system was developed for simulations. Simulation results revealed that in the analysis of the efficiency of a fivemass system, the effect of damping friction is paramount as compared to that of elastic coupling and clearance.
Keywords Fivemass system, electric drive, clearance, stiffness

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 twomass or multimass 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].
Systems with infinite stiffness and without clearance are qualified as onemass systems and are quite well analysed. Complex systems with more than one mass coupling between the driving source and connected loads are known as multi mass systems. Mostly, the simplification as a onemass 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 multimass system modelling.
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
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 fivemass system having damping friction, elastic coupling and clearance.

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 multimass systems. Onemass systems serve as basis for modelling electromechanical systems but are not popular due to their limitations and deviations from reality [5], [4]. Two mass systems are very popular and well analysed due to their simplicity and easy modelling with little deviation from reality. Threemass system models have few literature related to them, though they prove to be better and closer to reality as compared to a twomass system [6].
Works on fivemass systems however, are nonexistent in the literature. Systems such as helicopter control mechanism and ball mill drives are some examples of fivemass systems. Therefore, lack of relevant literature on fivemass system models calls for further research to extend and improve upon the quality of the existing models of twomass and threemass systems.

METHODS USED
Fivemass 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].

Schematic Diagram of a Fivemass System
A schematic diagram of a fivemass system having elastic coupling, clearance and damping friction is shown in Fig. 1.
Tr1 , T12
C12
12
Tr2 , T23
C23
23
Tr3 , T34
C34
34
Tr4 ,T45
C45
45
Tr5
J1 J2 J3 J4 J5
b1
T, 1
T12 , 2
T23
, 3
T34
b5
, 4
T45
, 5
Fig. 1 A Schematic Diagram of a FiveMass System having Damping Friction, Elastic Coupling and Clearance
The fivemass 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
C23
s (
T23
) Y23
(7)
respectively. Moment of inertia J2, J3, and J4
represent the 2 3
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
C34
s
C45
T34
(3 4 )
T45
Y34
(8)
(9)
between masses 1 and 2, 2 and 3, 3 and 4, and 4 and 5
s (
) Y45
respectively. The speed of rotation, 1
and 5
of electric 4 5
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
The corresponding transfer functions were used to develop a block diagram of the fivemass electromechanical system for efficiency investigations as shown in Fig. 2.
3, 3 and 4, and 4 and 5 respectively. The damping coefficients
of the prime mover and the load are denoted by respectively.

Mathematical Model of the Fivemass System
b1 and b5
T12
G1(s)
1
_
Y12(s)
T23
G2(s)
1
_
Y23(s)
T34
G3(s)
1
_
Y34(s)
T45
G4(s)
1
_
C23
C12
Y45(s)
G5(s)
1
Based on Newtons law of rotational motion, the mathematical model of the Fivemass 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:
T
J1sb1
_
Tr
C34
_ _ _
J2s
s
s
2 3
Tr2
_ _
s
J3s
4
Tr3
_
Tr4
5
J5sb5
J4s
s
C45
_ _
5
Tr5
1
G (s) 1 1
(1)
Fig. 2 Block Diagram of the Ball Mill Drive as a FiveMass Electromechanical System having Damping Friction, Elastic Coupling and
T Tr1
G (s)
T12
2

b12
1
J1s b1
(2)
Clearance


Simulations
2
G3 (s)
G 4 (s)
T12
T23
T34

Tr2
3

Tr3
4

Tr4
T23
T34
T45
J 2s
1
J3s
1
J 4s
1
(3)
(4)
Fig. 3 represents a MATLAB Simulink model of the five mass 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
5
G (s) 5
(5)
of the fivemass system model. The scenarios considered are as
T45

Tr5

b55
J5s b5
follows:

Varying damping coefficients at constant stiffness and
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:
clearance parameters.

Varying stiffness values at constant damping and clearance parameters.
C12
s
(1
T12
2 )
Y12
(6)

Varying clearance parameters at constant stiffness and damping friction.

Fig. 3 Simulink Model of the Fivemass System having Damping Friction, Elastic Coupling and Clearance
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].
It is convenient to investigate dynamic characteristics of the fivemass system in Simulink because it provides the possibility to consider nonlinearity of any type.
Table 1 shows the preferred standard parameters used for the simulation of the fivemass system model. These parameters were varied in various scenarios to identify the

Simulation Results
The results of input and output power as well as efficiencies of simulations of the generic fivemass system model are presented in Fig. 4 to Fig. 7.
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.
influence of damping friction, elastic coupling and clearance on the efficiency of the system.
Table 1: Standard Parameters of Simulations

b1 = 3, b5 = 10, in Nm/rad/s
b) b1 = 80, b5 = 100, in Nm/rad/s
P1 = 1264 W P0 = 664.3 W
P1 = 1264 W P0 = 646.5 W
Powe r Consumption (W)
Parameter
Value
Unit
Step Input Torque, T
100
Nm
Stiffness Coefficient, C12
50,000
Nm/rad
Stiffness Coefficient, C23
60,000
Nm/rad
Stiffness Coefficient, C34
3,000
Nm/rad
Stiffness Coefficient, C45
3,000
Nm/rad
Clearance, 12
5
mm
Clearance, 23
8
mm
Clearance, 34
5
mm
Clearance, 45
8
mm
Damping Friction of Motor (b1)
3
Nm/rad/s
Damping Friction of Load (b5)
10
Nm/rad/s
c) b = 3, b = 60, in Nm/rad/s
1 5 P1 = 1264 W P0 = 1089.3 W



RESULTS AND DISCUSSIONS
Efficie ncy (%)
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
d) a 52.54%
Time (s)
b 51.07%
c 86.11%
stability of the fivemass system.
Fig. 4 Varying Damping Coefficients at Constant Stiffness and Clearance
Power Consumption (W)
a) P1 = 1265 W P0 = 1089.3 W C12 = 50000, C23 = 60000, C34 = 3000, C45 = 3000, in Nm/rad
P1 = 1265 W P0 = 1090 W

50% increase of C12, C23, C34 and C45
J5 = 20 kgm2
J5 = 10 kgm2
J5 = 5 kgm2
J5 = 1 kgm2
Power Consumption (W)
50% decrease of C , C , C and C
P0 = 1894 W at J5 = 20 kgm2
12 23 34 45
P0 = 1539 W at J5 = 10 kgm2
c) P1 = 1265 W
P0 = 1088 W P0 = 1241 W at J5 = 5 kgm2
P0 = 1130 W at J5 = 1 kgm2
Efficiency (%)
Efficiency
a 86.11%
d)
Time (s)
b 86.13%
c 86.03%
Time (s)
Fig. 7 Varying Mass 5 (Load) at Constant Stiffness, Damping Friction and Clearance Coefficients
B) Discussions of Simulation Results
Fig. 5 Varying Stiffness Values at Constant Damping and Clearance Parameter
P1 = 1265 W P0 = 1089.3 W
Power Consumption (%)
a) 12 5,23 8, 34 5, 45 8, inmm
100% increase of 12 , 23, 34, 45
b) P1 = 1265 W P0 = 1088.5 W
80% decrease of 12, 23, 34, 45
The simulation results of Fig. 4 showed that damping friction had the greatest influence on the efficiency of the generic fivemass system model. For an input power of 1264 W, relatively high damping coefficients of b1 = 80 Nm/rad/s and b5 = 100 Nm/rad/s resulted in a very low output power of

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
Efficiency (%)
c)
Efficiency
d)
P1 = 1265 W P0 = 1088.9 W
a 86.11%, b 86.05%, c 86.08%
Time (s)
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 fivemass 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 te output power to 1090 W
Fig. 6 Varying Clearance Values at Constant Stiffness and Damping Coefficients
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 =
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 fivemass 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 systems 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.


CONCLUSIONS
Based on the findings of the generic fivemass system model, it can be concluded that:

Very low and very high damping coefficients result in poor efficiency whilst moderate damping coefficients give efficiencies more than 85%.

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 fivemass system. Thus, the lower the stiffness value, the less stable the system.

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%.

The more the load inertia, the higher goes the power consumption and more unstable the fivemass mechanical system becomes.
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