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International Journal of Engineering, Management & Sciences (IJEMS) ISSN-2348 –3733, Volume-1, Issue-9, September 2014

Dynamic Behavior of Electromechanical Linear Actuators by Using Unified Approach of Bond Graph Ashok Sharma, Ankur Dutt Sharma  Abstract— The study of the dynamics of a real system requires the modeling of the system. Models of the systems are simplified, abstracted constructs used to predict their behavior.

Using the language of bond graph, one may construct models of all type of physical systems. The models will be mathematical models represented by uniform graphical notation and a small set of ideal elements.

In this paper the dynamic behavior of electromechanical linear actuators is being discussed with the motive is to develop a universal model by using unified approach of bond graph that gives the opportunity to simulate both existing and new systems without having to remodel the entire system each time. The work refers to analyze the functional parameters of electromechanical linear actuators by modeling of different components of EMLA using bond graph. Given a bond graph model, causality can be assigned and algebraic-differential equations can then be obtained in an algorithmic way.

Index Terms— Electromechanical linear actuators, Bond Graph, Angular Momentum, Commutator.

I. INTRODUCTION Today’s extremely disturbed world where the risk constitutes the rule and the environment becomes increasingly dynamic, unstable and demanding, the modeling of manufacturing systems, companies, transport or even in supply chain, the mutual interaction of multi-natural phenomenon and the association of components caused by different disciplines.

The industrial processes modify the characteristics of raw materials using natural physical laws, the process dynamics can be described using energy and mass conservation laws, which can then be expressed as a mathematical model, such as a state space description. Since the manufacturing systems typically include non-linear elements, simulation is a valuable tool for studying these systems and predicting time responses.

Electromechanical linear actuators (EMLAs) are part of the intelligent flexible manufacturing systems and very promising with respect to fulfill special requirements, e.g. automatic operating mode, power management, reliability, maintainability which impose new concepts of design in applications requiring some effort and a clean environment.

It would appear that bond graph techniques can very usefully Manuscript received September 09, 2014 Ashok Sharma, Lecturer, Department of Mechanical Engineering, Govt. R.C. Khaitan Polytechnic College, Jaipur , Rajasthan, India Ankur Dutt Sharma, Assoc. Prof. , Department of Mechanical Engineering, Apex Institute of Engineering & Technology, Jaipur, Rajasthan , India

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be applied to such systems due to their suitability for symbolic analysis and their ability to include non-linear components.

[3]The bond graph is a graphical approach for modeling, based on the concept of power, and the systems are modeled as a set of elements which exchange energy in a power-conserving way.

II. SIGNIFICANCE OF BOND GRAPH APPROACH TO MODEL A MANUFACTURING SYSTEM The Bond Graph approach seems like a well adapted tool to the modeling of the manufacturing systems for the following reasons; (i) Utility of the language for any field, which facilitates the study of the manufacturing systems which are dynamic, multi-field, combinations, complex and diverse systems which integrates several fields . (ii) Give a great facility of modeling due to its graphic character which remains closer to that of the phenomenon to study (provisioning, transfer, storage, transformation, assembly, dissipation, conversion, distribution, etc). (iii) The Possibility of directly materialize the principal flows moving in the system (product flow, information flow and financial flow) by the intermediary of the power variables. (iv) The Possibility to refine the model obtained by addition of simple new elements bond graph without having to represent the step of modeling since the beginning. It allows on the one hand a correction in real time of the design phase and on the other hand to follow the modifications of the structure of the system due to new situations.

III. PROPOSED MODEL OF EMLA The EMLA model is built up by modeling the individual energy port as subsystem bond graph model and then synthesizing them into one system model.

A. Electrical port of dc motor used in EMLA The phase is excited by an external voltage source which is represented by effort source, Se. Current then flows through the winding. A part of the input energy is lost as winding thermal losses represented by a lumped dissipative element, represented by R-field. The effort source and the R-field are connected at a one-junction.

Figure 1: Bond graph model of electric port of DC motor

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Dynamic Behavior of Electromechanical Linear Actuators by Using Unified Approach of Bond Graph

B.Mechanical port of dc motor used in EMLA

load

R : R5

23

1

anti rotation of nut

R : R4

screw and nut

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worm and worm wheel

13

R : R2

TF

14

0

rotor

9

R : R1

TF

dc motor

GY

ke ..

R :R

3

constant voltage source

Figure 6: Proposed bond graph model of EMLA

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20-sim4.1 Viewer (c) CLP 2011

MSe

1

1

4 2

I : La

E.Model of screw nut system of EMLA The screw nut system converts angular rotation of screw shaft, to linear motion of nut and rod, and provide linear displacement of load to desired position.

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kt ..

Figure 4: Bond graph presentation of gear box of EMLA

GY

7

5

8

1

I : L1

10

1 ..

11

12

C :k

Gear is a transformer element which is used to transmit the torque of shaft of dc motor to screw shaft of EMLA. It may be a bevel, spur gear arrangement or may be a worm and worm wheel arrangement depending upon various geometrical configurations of EMLA. Figure 4 shows a bond graph model of gear box. Here C and R element represents the stiffness and friction loss between gears during motion.

l / 2pi ..

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D. Model of gear box

R : R3

20

0

16

Figure 3: Bond graph model of DC motor

1

I : L2

18

19

C : k1

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C. Model of DC motor used in EMLA A typical DC motor has a field winding and an armature winding mounted on the shaft. It also has a commutator that keeps the two magnetic fields at quadrature to each other. A DC motor’s model is shown in Figure 3.

The screw – nut system is considered as a perfect rotation to translation power transformer TF of lead l (ratio l/2pi). The nut-screw friction is considered as R effect that is modulated by the rod axial force. Inertias associated with functional motion are also introduced as I element (nut inertia, screw mass). The bond graph presentation is shown in figure 5.

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Figure 2: Bond graph model of mechanical port of DC motor

Figure 5: Bond graph presentation of screw – nut system of EMLA

I : L3

Shaft of the motor represents the mechanical energy port of the DC motor. Inertia is represented by the inertial element I and the bearing, windage and other losses by the dissipative port R. All the elements are connected together at one-junction signifying common speed as flow variable.

F. Equation steps of proposed model

International Journal of Engineering, Management & Sciences (IJEMS) ISSN-2348 –3733, Volume-1, Issue-9, September 2014 motor will remain same. The various plots between different variables of EMLA are being discussed in this section.

1. Define the state variables: The momentum associated with a mass (or inductor) and the position of a spring (or charge in a capacitor) is the generalized state variables used in the set of first order differential equations. The number of first order equations will be the same as the number of integrally causaled storage element.

The state variables for proposed model are as below:

The plot of total torque with respect to angular displacement is shown in figure 7. We observe from the figure that, initially the torque is higher. This is due to higher current at the beginning. As soon as the motor attain constant speed, the torque is stabilized as shown above; hence the motor will continuously run till the power supply is ON. The total torque is counter balanced by the frictional torque. This results in constant torque which only fluctuates around zero line.

p2, state variable for I element (electrical momentum) q12, state variable for C element (displacement) p8, state variable for I1 element (angular momentum of rotor) q19, state variable for C1 element (displacement) p16, state variable for I2 element (momentum of nut) p22, state variable for I3 element (momentum of load, rod) 2. Define various parameters used to simulate the model: the various parameters for electrical dc motor, gear ratio, parameters for nut and screw mechanism etc are set to simulate the model. The various parameters used in this Paper are given below: La = .000832 terminal inductance (H) J = 10.5 X 10-5 rotor inertia (kgm2) I2 = .3 mass of nut (kg) N = 4150 nominal speed (rpm) P =1 number of pole pairs Rs = 7.31 terminal resistance (ohm) K = (1.5) X 10-8 stiffness of screw shaft (N/m) k1 = 3 X 10-8 stiffness of nut (N/m) kt = .044 torque constant (Nm/Amp) ke = 1/217 back emf constant (V/rpm) fc = .0178 coulomb friction (N) fs = .089 static friction (N) fv = .002 viscous friction (N) R3 = 0.3 friction between nut and screw (0.1 to 0.3 for acme screw, .01 to .002 for ball screw) E = 24 input dc voltage (V) tr = 1 gear ratio l = 5/1000 lead of screw = pitch of screw for single start (m) I3 = 5 load (N) 3. Draw the equations: Draw the static and dynamic equations by using the inherent properties of elements and concept of causality. The notation en is used for effort variable in nth power bond and fn for flow variable in nth (n = 1 to 23) power bond as numbering given in proposed bond graph model of EMLA. IV. ANALYSIS OF RESULTS The simulations are done in MATLAB using the default solver ode45. The simulation time has been taken as 0.2 seconds, because beyond 0.2 seconds the characteristics of

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Figure 7: Plots of torque v/s angular displacement

Figure 8: Plot of angular displacement v/s time Figure 8 shows that angular displacement is linearly increasing with time. This proves that rotor is continuously running properly.

Figure 9: Plot of angular momentum of rotor v/s time In figure 9, angular momentum of rotor is shown. It is clear from the figure that angular momentum of rotor remains constant beyond .01 sec. The reason for increasing angular momentum before 0.01 second is that motor is accelerating in this interval. Thus the model so developed is appropriate.

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Dynamic Behavior of Electromechanical Linear Actuators by Using Unified Approach of Bond Graph

Figure 10: Plot of motor torque v/s time

Figure 13: Plot of linear velocity v/s time

The figure 10 shows the plot of motor torque v/s time. It is evident from figure that starting torque is very high and after some time as soon as the motor attain a constant speed the torque is also constant at minimum level. The torque is uniformly fluctuating about zero. This validates the model presented here.

Figure 13 shows the plot between linear velocities of actuator v/s time. The velocity of actuator for any constant load applied is increased initially and after some time it will be constant

Figure 11: Armature current of motor v/s time

Figure 14: Plot of linear velocity v/s peak load

Figure 11 shows the plot of current v/s time of dc motor used in actuator. This is evident from the figure that the current required to start the motor is very high.

Figure 14 shows the plot between peak load v/s linear velocities of actuator at 0.2 second. The figure shows that linear velocity of actuator decreases as the load on actuator increases.

V. CONCLUSIONS The application of electromechanical linear actuator (EMLA) has been grown significantly in recent year in the appliances industry and automotive industry. The fast growth of the EMLA in applications requiring positional and speed accuracy has increased the need for optimum and precise modeling of their dynamics and drive mechanism. Modeling of components of EMLA, dc motor and screw nut mechanism have been focused in this work.

Figure 12: Plot of angular speed v/s time.

The figure 12 shows that the angular speed of rotor is increasing up to 0.01 second because, motor is accelerating up to this value of time, and thereafter the rotor speed becomes constant. This is because after 0.01 second, other effects like back EMF and friction starts to act on the motor which counter balance the speed at a particular value depending on the supply voltage. This proves the speed characteristics of the motor.

The purpose of this work has been to advance the field of EMLA in production machines operating in a variety of operating conditions ranging from constant speed to continuous transient operation.

The performance of electromechanical actuator is analyzed in this Paper. The analysis of EMLA is carried out by developing the bond graph model of various components of actuator. For simulation of the bond graph model of EMLA, the software package MATLAB is used.

As a matter of fact the conventional modeling methods involve more computational work. The aim of Paper is to make a model that would be simple, accurate, easy to modify and suitable for real time implementation. The simulation

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International Journal of Engineering, Management & Sciences (IJEMS) ISSN-2348 –3733, Volume-1, Issue-9, September 2014 results of this work have shown that these goals have been [10]. Karnopp D.C., Margolis D.L, Rosenberg R.C.,th“System Dynamic – achieved. In this Paper, a unified approach of bond graph for Modeling and Simulation of Mechatronic Systems” 4 edition, John Wiley & Sons, INC, 2005. modeling of electromechanical actuator and its drive [11]. Margolis Donald, Shim Taehyun ,”A bond graph model incorporating mechanism is used, analyzed, and extended, for overcoming sensors, actuators, and vehicle dynamics for developing controllers for vehicle safety” Journal of the Franklin Institute, Volume 338, Issue 1, Pages the drawbacks of the conventional modeling approaches.

VI. FUTURE SCOPE OF THE WORK One of the advantages of the bond graph model of EMLA presented here is that it is not only complicated but improvements and additions are also very easy to make in the developed bond graph model.

21-34, January 2001 [12]. Antic Dragan, etc “An introduction to bond graph modeling of dynamic systems” IEEE trans., pp-661-664, 13-15 October, 1999 [13]. Kuang M.L., Fodor M, etc Ford Motor Company “Hydraulic brake system modeling and control for active control of vehicle dynamics” Proceeding of the American Control Conference San Diego, California, June 1999 IEEE [14] .www.bondgraphs.info

The purpose of bond graph model as developed in this Paper is to predict the behavior and performance of EMLA only, but the same can be implemented for modeling and simulation of a complete automation system. For example robot for assembly operations in which precise and accurate movement of each robotic joint is desired can be modeled by bond graph modeling. The complete model of dc motors, actuators and various drive mechanisms coupled with robotic system could be taken up for efficient modeling of the system.

Also detection of rotor and load faults in actuator operating under stationary and non stationary conditions can be taken up for detailed modeling and performance calculations of EMLA drive system. Although the research in this work has been limited to EMLA with nut- screw drive system, there are several different kinds of actuator which may be used in home appliances and automotive industries, could be modeled by the technique employed in this work.The research work presented in this Paper aimed at providing a system-level model of the EMLA. REFERENCES [1]. Junxia Li, Ziming Kou, "Modeling and Simulation of the Hydraulic Excitation System Based on the Power Bond Graph," Second International Conference on Computer Modeling and Simulation, 2010, vol. 4, pp.

234-237. IEEE 2010 [2]. Rai B. Umesh, etc “Bond graph toolbox for handling complex variable” IET Control Theory App. 2009, Vol.3, pp-551-560 [3]. W. Borutzky “Bond graph modeling and simulation of multidisciplinary systems – An introduction” Simulation Modeling Practice and Theory 17, 2009, pp 3–21 [4]. Samantaray A.K., Ghoshal S.K.,”Bicausal bond graphs for supervision: From fault detection and isolation to fault accommodation” Journal of the Franklin Institute, Volume 345, Issue-1, January2008, pp 1-28 [5]. Bouamama B. Ould “Automatic generation of supervision system based on bond graph tool” 5th International Symposium on Mechatronics and its Applications, 27-29 May 2008, Amman, pp 1-5 ISBN: 978-1-4244-2033-9.

IEEE 2008 [6]. Gawthrop Peter J., etc “Bond – Graph Modeling, a tutorial introduction for control engineers” IEEE control system magazine, April 2007, pp 24-45 [7]. Khurshid A. and Malik M.A. “Bond graph modeling and simulation of impact dynamics of a car crash” Proceeding of International Bhurban Conference on Applied Sciences and Technology Islamabad, Pakistan 8th-11th January, 2007 IEEE [8]. Kayani S.A. Malik M.A., “Modeling and simulation of biped kinematics using bond-graphs” This paper appears in: Emerging Technologies, 2006. ICET '06. International Conference, Publication Date: 13-14 Nov. 2006 pp 677-682 [9]. Xiyun Yang, Yuegang lv etc “Research on boiler drum dynamic model with bond graph” proceedings of the First International Conference on Innovative Computing, Information and Control 2006 IEEE

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