THE DYNAMIC PARAMETERS IN DESIGNING OF LINEAR ELECTROMECHANIC ACTUATORS

7/29/2019 THE DYNAMIC PARAMETERS IN DESIGNING OF LINEAR ELECTROMECHANIC ACTUATORS

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Proceedings in

MANUFACTURING

SYSTEMSProceedings in Manufacturing Systems, Vol. 5 (2010), No.

THE DYNAMIC PARAMETERSIN DESIGNING

OF LINEAR ELECTROMECHANIC ACTUATORS

Vasile NASUI1, Radu COTETIU2, Mircea LOBONTIU3, Nicolae UNGUREANU4

Abstract: This paper presents the basic concern of the creators of systems of electro mechanic actuators

type of improving their dynamic performances by an appropriate constructive achievement of the

transforming mechanism of rotation and translation movement giving priority to the ball-screw

mechanism. The acting directions are shown in order to improve the parameters such as increasing

speeds and portent capacity which generate the necessity of the analysis and the solution to some

problems concerning the dynamics of the systems.

Key words: electromechanic actuator, virtual simulation, modular robot, dynamic modeling

1. INTRODUCTION

Lately almost in all the technological processes and in

the industrial production based on machine constructionthe issue of a high economic efficiency has always been

raised [2]. In spite of the fact that the electronic

equipment is relatively highly developed, the advantagesof using actuators instead of the classical systems of

acting application friendly are obvious. By studyingcritically the evolution of the actuators mechanism we

notice the evolution directions of the improvements. The

direct effect of the insertion forces are the vibratingforces which increase the mechanic stress and thekinematics elements and has a direct effect worse

geometric parameters of the acting mechanic system [1].The taking into account that this negative effect of the

insertion forces is higher being in direct relationship ofthe increased functioning speeds of the actuators. In this

context, the introduction of the electro mechanicactuators can be achieved only in the case of superior

performances which have been achieved lately owing tonew solutions of actuator mechanism. The diversity of

physical phenomena which constitute the basis forconstructive materialization of the actuators opens new

horizons in researches taking into consideration newphysical principles and new materials which fulfill theacting requirements in the field of mechanic engineering

[3]. The modular mechanical rot translation systems

represent a new concept in mechanical transmissions ofvarious types and destinations that efficiently replace

classical systems mechanically, hydraulically andpneumatically activated. These provide the optimal

solution for the construction of quantitative andqualitative mechanical transmissions due to a wide range

of usage, high efficiency, cinematic, dynamic capacitiesand high precision [5].

In the componence of industrial mechanical equipment

there is a high constructive diversity and types oftransmissions that are to be analyzed individually atdesign, as there is no unitary selection, synthesis and

control methodology for them at the hand of designers.

The main problem for the conceiving of optimal

transmissions that should lead to well performingmachines and equipment as these have an essential

contribution to the achievement of constructivequalitative parameters and functional ones, including

those on energetic efficiency. It is known that in thefield of the mechatronic actuators acting systems are

minimized this they become really small. These types ofactuators have specific functional characteristics superior

to the characteristics of the conventional actuators such

as: the report power/weight or power/ loading. The

lasting period of functioning, high efficiency, largeregulating range of the movement parameters, the

functioning security, the constructive simplicity, the highaccuracy of positioning are compact etc. [5].

An actuator's function is to provide thrust andpositioning in machines used for production or testing.

One type is the electromechanical actuator, whichconverts the torque of an electric rotary motor into linear

mechanical thrust. The technical system of the linearactuator perfected through this method has a few basic

characteristics expressed by particular indicators such as:adjustable acting, high precision, and efficiency portent

capacity, a rank of high speeds, numerical control etc

A new innovative and original structure of a type oflinear actuator is presented in the figure 1 in which theextension and the conversion of the energy is

accompanied by the conversion of some informativesignals [6].


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V. NASUIet al. / Proceedings in Manufacturing Systems, Vol. 5(2010), No. 1 /110 (8 pt, Italic) 2

Fig. 1: Band stretching mechanism actuator

Although the actuators have a great functional and

constructive variety, in general they have the followingcharacteristics basic structure consists of electric motor,

drive mechanism for converting rotary motion intotranslation and its control system. This offers the best

solution to linear actions owing to the large flexibility to

the high efficiency to the cinematic, dynamic and highprecision capacities [4]

2. THE DISCRETE PATTERN OF CALCULUS OF

THE DYNAMIC OF THE ACTUATOR

For any type machine, device or shifting system, it is

important to increase by percentage the real workingtime, which leads to the main aimed parameter in

manufacturing the actuators such as velocity. Besides the

parameters of the actuators there are also the dynamiccapacity and the efficiency [4].

The main preoccupation of the actuators

manufactures is to achieve extreme working speeds veryhigh and very low. These two directions create thenecessity of analysis and the solution to some problems

given by the type of acting, the weight, the positioningprecision, the functioning safety, the frame, the fiability.

The optimum for the actuators is done starting fromthe acting time analysis, the imposed technological

requirements. Once these parameters are established,then priority is also established, after that follows the

synthesis of the mechanism of movement transformation.In this synthesis, the input data are the above mentioned

parameters and the output data are the dimensions of thecomposing elements, their dynamic behavior, the

distribution of masses etc [4].The main dynamic criteria of the optimizations of

the mechanism of movement transformations, which are

useful in assessing in the appreciation of the quality ofthe functioning of the actuator mechanism in working

regime: the average mechanic efficiency, the losses in

kinematics couples, the multiplication coefficient of theforce, the coefficient of the non-uniformity of the

working, the static and dynamic losses of balance.The average coefficient of the non-uniformity of the

working, by taking into account the movement equation

(1) as energy equation:

( )2min

2

maxmax2

1 = redJL (1)

where Lmax is the excedentary mechanic working, results,the coefficient of the non-uniformity of the working,

2

max

medredJ

L

= (2)

where:Jred are inertia of motor plus load [kg.m

2];

max, min, - the value of extreme velocity of theangular velocity of the reduction element [rad/s];

med - the average value of velocity [rad/s].

The requirements of the mechanic construction ofthe actuator are more often dynamic, which give birth

acceleration of the movement and of the force of inertiawhich can cause vibrations in the end. If the system is

put out of its state of stability due to an impulse and ifthis impulse is eliminated, then the system executes free

oscillations, during which, there is a continuous

exchange of kinetics and energy of distortion. In the caseof continuous action of the disturbing force, the systemexecutes forced oscillations.

The degree of stress on the component elements ofthe electro mechanic linear actuators is represented by

dynamic coefficients. These should be taken into

consideration functioning. According to these dynamic

loading coefficients we can appreciate pretty well theendurance of the actuator and the degree of their loading.

On the basis of the dynamic coefficient we canfollow: the exact limitation of the work purpose,

according to the maximum dynamic loading whichappears within the flexible links in the mechanisms, the

values of the maximum accelerations and of theminimum functioning time in the period of the start-up,

of braking and the frequencies of oscillation of thesupports [5].

The report between the value of a dynamic factor Sdinas the example force interior and the shifts caused by

force P(t), a statically factor oaring to the force whichacts statically is called dynamic coefficient,

.st

dindin

s

sk = . (3)

Owing to the fact that when constructing theactuator there are always forces of resistance (example

interior forces of friction) which absorb the energy, thefree oscillations are not infinite, but amortized in time.

The damping factor influences the oscillations of theforce in particular the dynamic coefficient. The simplest

way for these is with a degree of freedom (the masssuspended don a spring without mass) and required by

the disturbing force P(t), which represent an arbitraryfunction of time.

The parameters which characterize the economicregime are the training electric power and the efficiency

of all the structural components in the mechanical

transmission with screw-nut mechanisms of slidingfriction or rolling, the experimental research [5], toextract the following relationship for efficiency:

p

dk+

=

1

1

(4)

where:d is the diameter of the screw;

p - thread screw propeller pitch;k - dependent constant construction of

transmission, depending on how friction, namely:k = 0.33, for sliding k = 0, 033, for rolling.


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The elastic pattern has at its basis the analysis ofthe deformations of the cinematic couples where the ball

screw mechanism has a great importance.The deformation can be considered according to the

axial force where:

z

Q

Pd=

31

4,1[m] (5)

where:Q is axial force;

P - pre-load force;z - number of balls;

d1 - the nominal diameter of the balls;

- the contact angle of the balls;

- the angle of the sloping the propeller of thescrew;

For this, we make real assessment of the value of theefficiency of the actuators transmission considering the

overall of the power losses within the actuator and for

partial loading [8].For the transitory regimes of functioning, the

efficiency can be calculated deterring the two

components of the moment of losses within thetransmission according to the relation (4) including the

dynamic moment. The experimental determination ofpower losses specific to the mechanical transmission of

an actuator has shown its dependence according to thedegree of loading and functioning regime. The trial stand

of industrial linear actuator is presented in the figure 2.

dr .ing.Nas ui Vas i le

STAND PENTRU NCERCA R E A M E C A NI SM ELOR DERO T O - T R A N S LA T IE

S a b o u D i n u

SR 2 5 x 1

UM[mm]

A3 ( 4 2 0 x 2 9 7 )

U N I V E R S I T A T E ADE NOR DB AIA MAR E

Pl ansanr: 1/ 2

A p r o b atVeri fi c at

D e s e n atPr oi ect at

D a t a:15. 06.2 0 0 4

1 :1S a b o u D i n udr .ing.Nas ui Vas i le

S R 2 5 x 1S R 2 5 x 1S T A S 5 9 8 2 - 7 4S R 2 5 x 1S R 2 5 x 1S R 2 5 x 1S R 2 5 x 12 /2S R 2 5 x 1S R 2 5 x 1S R 2 5 x 1S R 2 5 x 1S R 2 5 x 1S R 2 5 x 1

S R 2 5 x 1S R 2 5 x 1S R 2 5 x 1S R 2 5 x 1

ISO 4 0 1 4 -9 4S A T S 4 0 7 1 - 8 4S T A S 7 6 6 0 - 8 2

Fig. 2. The trial stand for electro mechanic actuator

The Mat Lab Simulink programmed allows the

creation of the dynamic patterns by using some blocks

and subsystems which define that particular pattern, forthis, its necessary to know very the system to by

modeled, and of the physical and mathematical lows,according to which the system works [6].

The blocks which can be used, are found in the

library within the programmed are we can define orcreate other blocks or we can turn to the use of external

functions used in the Mat Lab program (fig. 3).After creating the model, this is circulated, and the

simulation can be visualized using a display where wecan read the numerical values of the analyzed signal or

the signal can be analyzed by using the graphics with theaid of one of the blokes of type SCOPE, this making

possible the analysis of the results.For the moment of training the screw, we need the

average force with we load the system, the pace of thescrew and the efficiency which the screw on rolls offers.

For the calculus of the acceleration moment, thealgorithm of calculus differ, having more values and at

different moments of the circuit while calculating theangular acceleration, the reduced insertion moment of the

engine shaft, the insertion moment of the screw, theangular speed, the linear speed, the pace of the screw, the

inert ion moment of the engine and the necessary

turation.To enable us to see these equation under a simpleshape, the Mat Lab Simulink program which gives us the

possibility to insert these in so-called subsystems, wherethey will work in the same way but we le have the

possibility to insert other values wile go out of the

subsystems being added in an adder which wile give the

total moment, for the operation of the rot translationsystems. The chosen mathematical model is extremely

sensitive to the change in the alignment parameters, afact that confirms the possibility of its successful use in

the procedures of virtual simulation by the support MatLab Simulink[7].

Transposing this model which visualizes theequation under a simpler program Mat lab gives the

possibility of introducing them under the so-calledsubsystems, where they old work the same way having

the possibility of implementing some after valuesaccording to the pattern of the ball screw according to

figure 2.The pattern of calculus of the moment of training the

screw is presented in the figure 2.

1

The aurage force

2

XX

+

1

2000

X

0,85

Constant

The moment oftraining the screw

`

The pace of the screw

The eficancy of the transmission

Fig. 3. The pattern of calculus of the moment of training

3. THE CONTINUOUS CONTROL ALGORITHM

These restraints refer the achievement to the

possibility of achieving technical performances referringto the parameters of functional geometrical precision.

These are essential in the case of using positioningsystems from robots, machine-tools computer controlled,

specific to transitory conditions with frequent speedingand braking, starting and stopping at a. fixed point

A block diagram of the system (fig. 1) is shownbelow (fig. 3).

We observe that the equations are the some;therefore, we can establish correspondence among the

analogous parameters which allow solving electricalcircuits dynamics problems by the theoretical and

experimental methods.


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The idealized equation for continuous controlalgorithm is,

[ ])())()()(0

tEdt

dkdttEktEktf d

t

ip ++= (6)

here:

F(t) is the output of the controller at time t;

kp the proportional gain constant;ki - the integral gain constant;kd the derivate gain constant;

E(t)- the error at time t.Below is block diagram (fig. 4) of the control system

in the continuous control form.For small sample times this equation can be turned

into a difference equation by discretization.The derivate term is replaced by a first-order

difference equation and the integral term is approximatedusing trapezoidal integration. This equation required

storage of past errors.

The intermediate equation can be transformed into arecursive equation where only the previous output,

current error, and last two errors must be stored.

Kp

Ki

Kd

GXP

Fig. 4. The continuous control block diagram

The final equation then takes the form

F(t) = F(t - 1) + k1 E(t) + k2 E(t - 1) + k3 E(t - 2) (7)

where:F(t - 1) is the previous control output;

E(t - 1)- the previous error;E(t - 2)- the error proceeding E(t - 1).

The Lab VIEW program allows the selection ofreal numbers for gain constants. These constants, along

with the sample frequency, are converted into K1, K2, K3according to the formula shown above.

T

kTkkk dip ++=

21 ,

2

22

idp

Tk

T

kkk += ,

(8)

,3T

kk d= T=

f

1

4. CONCLUSIONS (6 pt)

This research is part of the modern preoccupationsregarding the improvement of new systems of linear

acting and of numerical modeling using algorithms andprograms of numerical computation and virtual

instrumentation.The methodology of mechanic dynamic modeling

and that of virtual modeling which was approached led tothe measure convergence to the theoretical ones which

prove its efficiency and its correct choice. The research is

of great importance as the present calculation algorithmsregarding the main dynamic parameters, power andmechanical efficiency.

The achieved theoretical and experimentalresearches allowed the dynamic identification of the

electro mechanic linear actuators.

The work integrates itself into the present day

researches in the field of the development of the modernmechanic transmissions making contributions in their

optimal design. In the future the researches can continuefor the development of new applications on other types

of mechanical transmission using this method anddifferent modular control laboratory.

This results a characteristic of functioning specific toeach measure of translation unit according to the

dimension and the step of the moving screw with whichit is equipped. The development perspectives aim

optimum solutions equipped with mechanisms oftransmission and transformation of the movement with

high efficiency and fiability.

5. ACKNOWLEDGEMENTS

The authors make the best of the researches done

within the grant regarding the development of theactuators within the flexible systems of reworking in the

laboratory of the North University of Baia Mare. (10 pt)

6. REFERENCES (6 pt)[1]. Borangiu, Th.. Advanced Robot Motion Control, EdituraAGIR, Bucuresti, 2003.

[2]. Ispas, C., Predencea, N., Ghionea, A., Constantin, G.Machine Tools, Editura Tehnic. Bucharest, 1998.

[3]. Montgomery, D.C.Design of Analysis of Experiments, 4th

Edition, John Wiley & Sons, NewYork, 1996.

[4]. Maties, V. s.a. Actuatori in mecatronica (Theactuators inmechatronic, Editura Mediamira, Cluj - Napoca, 2000.

[5]. Nasui, V. Actuatori liniari electromecanici.Electromechanics linear actuators, Editura Risoprint, Cluj

Napoca,2006.[6]. Nasui, V.Actuator mechanism ntinzator de band.(Band

stretching mechanism actuator), Patent RO 122347, 2009.[7].John, J. Hall and Robert, L. Williams, I., Frank van Graas.Cartesian Control for the Inertial Measurement Unit

Calibration Platform. In: Motion & Control No. 8 (May 2000.,

Avionics Engineering Center Ohio University Athens, Ohio[8].***Integration of Animation, Simulation, and

Experimentationin a Modular Control Laboratory. Proceedingsof the 2003. Midwest Sectio Meeting, University of Missouri

Rolla 2003. American Society for Engineering Education

Author(s): (6 pt)

Dr.Vasile NASUI, Professor, Head of Department,

North University of Baia Mare. IngineeringSystem of Technological Management Departament.

E-mail: [email protected]
mailto:[email protected]:[email protected]


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Dr. Radu Cotetiu, Professor, North University of

Baia Mare, Faculty of Ingineering. Str.:V. Babes

No 62 A, 430083. Romania, E-mail: [email protected],

Dr.Mircea Lobontiu, Professor, North University

of Baia Mare, Str.: V. Babes No 62 A, 430083.

Romania, E-mail: [email protected]

Dr. Nicolae Ungureanu, Professor,North

University of Baia Mare, Faculty of Ingineering.

Str.: Dr. Victor Babes No62A. E-mail: nicolae.un

[email protected],
mailto:[email protected]:[email protected]:nicolae.un%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%[email protected]:nicolae.un%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%[email protected]:[email protected]:[email protected]:nicolae.un%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%[email protected]:nicolae.un%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%[email protected]

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THE DYNAMIC PARAMETERS IN DESIGNING OF LINEAR ELECTROMECHANIC ACTUATORS