Methodology of mechatronics system decomposition

Vol. 2, No. 2, pp. 199-206, 1992 Printed in Great Britain

0957-4158/92 $5.00+0.00 © 1992 Pergamon Press plc

Mechatronics

M E T H O D O L O G Y OF M E C H A T R O N I C S SYSTEM DECOMPOSITION

VLADIMIR ~OV

International Association for Research and Production ROBOT, nfim. Legionfirov 3,080 01 Pregov, Czechoslovakia

(Received 9 February 1991; accepted 11 September 1991) model of functions and interactions facilitates the decomposition of any mechanical or electronic devices and components as well as their mutual relations.

Abstraet--A

INTRODUCTION Mechatronics systems consist of a number of mechanisms, control, supervision and information components, the integration of which enables to obtain the desired machine or equipment functions. The optimum performance-reliability-costeffectiveness relation is one of the most significant qualitative parameters. Hence, the design of these systems presupposes techniques that would provide an optimum relation between automated functions and reliability. Attention must be paid to the problems of redundancy of mechanical, control, supervision and information units, too. As a whole, they represent a precondition for optimum performance and cost-effectiveness. These circumstances made the author of this paper look for available methods of decomposition into individual functions and interactions, with the aim to evaluate them from the point of view of their performance, reliability and cost-effectiveness. The principles of the theory of description of mechatronics systems based on functions and interactions can lean upon the theory of the Markov chain that is defined: (a) by a discrete set of states of the system

{$1, $2 . . . . .

Si}

(b) by an attached transition probability matrix

(pj~), where P/k is the transition probability from the j-state to the k-state. The Markov chain can be plotted by oriented graphs. An oriented graph is a pair of sets ({S~}{pjk}). Structural graphs are pairs of sets ({St}, {pjk}) with the initial $1 node. A detailed review of applications of the theory of systems and the theory of graphs is given in [1]. The most numerous applications of the theories can be found in the 199

200

V. COP

field of communication network control, hierarchical control, power systems, automated reliability control within various technological systems, etc.

A MODEL OF FUNCTIONS AND I N T E R A C T I O N S A model of functions and interactions facilitates the decomposition of any mechanical or electronic devices and components as well as their mutual relations. In addition, it is possible to proceed from the individual functions and interactions to higher levels represented by integrated equipment, subsystems and manufacturing systems. The model of function and interaction decomposition is given in Fig. 1. As far as the automated and non-automated processes are concerned, a unit operation can be identified with a function of a system component influencing the positional or mechanical object features. Then, an interaction can be conceived of as a unit operation with non-mechanical functions. The interaction represents an elementary functional link expressing relations, dependencies and mutual actions of

O1

-q~

- | i-ii i .

-

.

.

L-11112133 . . .

-m-q ~ -

.

.

J~S3

.

Hi . , .

__

Urn

-+t-t-t-t-t-t-t-t Fig. 1. The aggregation and sequential structuring of automated manufacturing systems. Graphic symbols: u--actions and functions of a device or an operator, u= f (technological, handling, control, information and monitoring functions), S--working cycle in automatic mode, S--can be represented by a device, a robot, control system, inspection and information system, AED (automated engineering design), transport and storage system, P--automated section, P--robotic technologicalworkplace, robotic technological complex, automated manufacturing system, O--automated manufacturing organism, O--CIM or an incomplete variant of the set of automated workplaces and devices.

Methodology of mechatronics system decomposition

201

the system element. Moreover, it specifies the order and the hierarchy of relations of a particular object. In this way, it is possible for any process to be described as a sequence of functions and interactions, whose integration can be technically circumscribed into a working operation, including: process operation within a working cycle; sequence of operations within a manufacturing island; and sequence of operations within a manufacturing system. The algebraic notation of the function and interaction structure within a multi-level system, making use of the graph theory, is as follows: G = (U, H), where U is a set of components, devices and subsystems and H is a set of interactions among the individual components, devices and subsystems. Figure 2 gives the diagram of decomposition of functions and interactions by the theory of oriented graphs. Description of automated system introduction (Fig. 2) by unatrix theory is as follows: U = {O1, PI, P3, S1, $2, $3, $4, Ss, . . . U1, U2, U3, U4, U5} H = {(O1, P1), (O~, P3), (PI, S,), (P,, $3), (P1, S.)(P3, Si), ($3, U2), ($1, UI) , (31, U3) , (3,, Ui) . . . . (Sn, U2) , (3n, Un) }.

The meaning of the symbols of individual operations (functions and interactions), process operations, sequence of working operations within a manufacturing system points to the system of integration of functions and interactions. A diagram of each integration stage can include the information about the number of functions and interactions required for executing the particular operation or sequence of operations. This approach enables us to produce a mathematical description and subsequent processing of acquired information. The theory of graphs enables us to express characteristics of the manufacturing system G as follows: (1) Sequences: a sequence of functions and devices u,, s~, Pi, Oi • u, where ui+l e r(ui). O1 PI~ S.//"

~

.............

4thI_evel

~

3rd level

P3 S2

$1

2nd level

1st level

Fig. 2. Description of automated system structure by the theory of oriented graphs.

202

V. (~OP

(2) Connections: the functions and devices ui, Si, Pi, Oi are interconnected and Si(ui, u2, u3 . . . ) Of(P1, P3) is called an oriented connection between the functions and the devices u~, O~. (3) Number of interactions, functions, devices characterizing a system size. (4) Path: a path in an oriented graph is a connection characterized by the relation u i ~ uj, where i, j = 1, 2 . . . If Ul = u2, then a path is closed--it is called a cycle. The oriented graph G can be represented by an incidence matrix. A graph applied for the description of an automated manufacturing device or system allows to specify: number of levels within a hierarchical automated system; number of subsystems, devices, functions and interactions in an automated system; and succession of functions, interactions and their integration to higher-level systems. The application of the method in evaluating the performance, reliability and cost-effectiveness enables us to use the theory of resistance for critical stresses. The critical interactions and functions can be determined from the relationship: Rw(t) = Kw x Rt,

where Kw is the significance coefficient of an interaction and a function within an operation, cycle and sequence of operations under evaluation and R t is the probability of a failure-free condition. The integral indicator of useful quality E , based upon the method of interactions and functions, enables us to evaluate the performance and cost-effectiveness in a complex way from the relationship: E-

WxK IFi × N i '

where Kj is the quality class coefficient, W is the performance parameter, I F i is the value of unit interaction and function, respectively, derived from R , , ( t ) and Ni is the unit cost per interaction or function.

D E C O M P O S I T I O N OF A ROBOTIC SYSTEM

The automated system decomposition technique is based on the analysis of their internal structure. A case in point is represented by the decomposition of automated systems such as process systems, process handling, in-process transport, control, check and information system, etc. A different decomposition procedure is represented by that of the internal structure of elementary functions and interactions as well as their optimum integrations to automated devices, up to the highest-level integration, i.e. fully automated manufacturing system. Examples of an automated device decomposition into elementary functions and interactions were mentioned in [2]: PR-16 industrial robot, AM1 manipulator, GS and T140 shock absorbers. The issues of robotic workplace decomposition were verified

Methodology of mechatronics system decomposition

203

too. The decomposition technique is based upon dividing an automated cycle into elementary functions and interactions. A function flow chart is the most advantageous technical principle. The next description level is represented by a graph of functions and interactions. See Table 1 for their application in the GS and T-140 shock absorbers. As far as the automated workplace is concerned, the most suitable principle for the decomposition into elementary functions and interactions is a cyclogram of the individual operations of a particular process. Decomposition of a robotic system is given in Fig. 3. The examples illustrate a robotic system design consisting of an industrial robot PR 16-P, two machine-tools SPN and a peripheral design (shaft magazine). A working cycle of a robotic workplace includes 72 operations, e.g. information signal and cycle starting - arm extention (HU) towards the SPN 1 - gripper closing removing a workpiece from the SPN 1 - arm withdrawing (HU) - etc. The working cycle analysis in the horizontal arm unit (HU) and the control system (Fig. 4). The arm (HU) motion requires 30 interactions and functions, the interaction of which within a sequence of a working cycle can be defined as follows: (a) transmission of a control and information signal of five interactions; (b) actuation of H U drive circuit aimed at executing of motion of six interactions and functions; (c) HU extension . . . 10 functions; Table I. Graph of element functions and interactions GS D a m p e r

P1 P2 P3 P4 P5 P6

-

T-140 D a m p e r

Buffer Piston rod Throttling body Accumulator Spring Check valve (flap)

P1 P2 P3 P4 P5

-

Buffer Piston rod Throttling body Accumulator Spring

Complete interaction relations within a graph of functions

P~ P2 P3 P4 P5 P~

PI

P2

P3

P4

P5

P~

150 0 0 0 511 0

112 210 0 0 0 612

0 213 310 0 0 0

0 0 314 410 0 0

115 0 0 415 550 0

0 0 0 4x6 0 610

Pl P? P3 P4 P5

P~

P2

P3

P4

Ps

110 0 0 0 511

112 210 0 0 0

0 213 310 413 0

115 0 314 4~0 0

0 0 0 415 550

204

V. (~OP

Fig. 3.

(d) actuation of the drive circuit to stop the motion . . . five functions and interactions; and (e) transmission of a control and information signal . . . four interactions. The decomposition of a working cycle within a robotic system confirms the initial assumption that it is an industrial robot that has the highest level of loading with 90% of functions and interactions. Within a robot it is a horizontal unit with 41.6% interactions and functions of a robot. The working cycle of the horizontal unit itself is dominated by interactions and functions of the drive circuit and the direct function of extention representing 2/3 of the total. Based upon the probability of reliability and the weight of the individual functions and interactions, the resulting critical parameters of the function Rw(t) are concentrated in the groups (c) and (d), i.e. in the function of the stop, damper and arrest mechanisms

Rw(t) =

0.28,

in interaction with actuation of the drive unit

R.(t)

= 0.22.

The other groups of functions and interactions have significantly lesser influence on the occurrence of critical states. Values of the function Rw(t) = 0.099-1.5.

Methodology of mechatronics system decomposition

jz

205

Application of the model of interactions to the PR 16-P horizontal unit

"X Y

S×

Additional information Input: B 41 (3005) stop signal B 42 (3006) counting signal H (2048) desired value register Auxiliary: H 1 (2136) 'extension' position counter register F1,2,3(3056 57-58) service bit Z 9 (2104) m e m o r y R 2 (2112) position register T 1 (3176) timer for extension Output: Y 41 (3029) switchboard - extension Y 42 (3030) switchboard return motion Y 43 (3031) switchboard detent Y 44 (3032) switchboard finger Program length: 75 words Average frequency (time) of an instruction: 3 ~sec

Program flow diagram

Fot,o:41 I otio1 I

1-1-4

[.

"1 "--~Y42 I

Release ~Y43

"'1"

<>

Dwell v3 finger "1 '-Y44

H1 - 1 *H1

Dwell vl Arrest "0" ~Y43 I Dwell T2 42 0 ' ~Y41, [

H1 + 1--H1[ i

I "1"~12

Bring ~ ] request

+ Fig. 4. CONCLUSION

The peculiarity of applications of the mechatronics system decomposition techniques exists in three fields according to our experience. The first field is related to optimization of automated device and system designs from the point of view of combination of systematically incompatible components of

206

V. (~OP

an automated device or system. The theory of functions and interactions provides a basis for the standardization of the internal structure analysis methods. The second field is related to automation of engineering and designing operations by means of C A D / C A M , where graphical, symbolic, and coding representations of internal functions, interactions and structures allow us to find useful means for simulation of optimization tasks. The third field results from the standardization approaches to mechatronics systems. The development of databases, algebraic and graphical notations of multilevel systems, including hierarchical connections and relations are important principles for internationally accepted information exchange systems and for international standards in the field of mechatronics systems.

REFERENCES 1. Beneg J., Theory of Systems. Academia, Prague (1974). 2. (~op V., Contribution to quality improvement and automation level development in robotic technological systems, Doctor degree paper. Pregov (1985).