Objective method for assembly.

Vaclav, Stefan ; Peterka, Jozef ; Pokorny, Peter 等

Abstract: The known methods of DFA brought a lot of good solutions of design as considered from the point of view of assembly. However they are criticized that the used rules are too general and the attained results are evaluated less objectively using marks or calculating of so-called relative expenses, which are depended on changing economical situation. OMA is complementary method to all known methods of DFA. OMA describes assembly, according to the theory of systems as a subsystem of the production system, whose aim is to achieve profit in assembly. Design of product is only one factor in the way to achieve the goal. The known rules and examples of DFA give new ideas but they do not give instructions how to realize them in order to make assembly structure trouble free assembled and functionally perfect. Instead of subjective marking by evaluation of results, OMA offers to use three objective criteria: the sum of assembly paths, the number of assembly actuators, and so-called grade of intelligence of assembly task.

Key words: Assembly, DFA, Design, Theory of Systems.

1. WHAT IS THE ASSEMBLY?

Assembly according to the theory of systems (cybernetics) is described on the fig.1. Most important is the definition of the aim of the searched system (fig.1). Undoubtedly the aim is profit, as in others branches of enterprise.

[FIGURE 1 OMITTED]

The aim of perfection of assembly is not only perfection of the all inside and outside factors influencing the profit separately, but also of all of them in reciprocal relations. Automation is not the main aim of our effort, it is only one of the known means to increase profit and quality.

2. KINEMATICAL PAIRS

We will limit ourselves here to problem of assembly of mechanical structures. These consist of kinematical pairs of different grades of movability and of solid members connected with over given pairs. The examples of kinematical pairs are on fig. 2. Every pair is drawn in its real form and in the form of so called ball model.

[FIGURE 2 OMITTED]

Ball model is fiction of the real pair in which the real contact plains are replaced by point contacts realized so that one of the bodies is created only by balls and is contacted with second body only in points. All the statics is based on imagination, that bodies are contacted only in discrete points, where they participate in discrete reactions (Valentovie 1996).

We can apply the static analyze only on the statically determinite structure. The analysed pair will be statically determinate only if the number of contact points (discrete contact reactions) ([SIGMA]k) and the number of possible movements

([SIGMA]m) will sum up d = 6. d = [SIGMA]k + [SIGMA]m (1)

In the line 2 fig. 2 are analyzed two translational pairs (2a and 2c). The ball model 2b of pair 2a shows that the pair has 5 contact points and one possible movement (translation). The sum of these values (d) is 6--the pair 2a is statically determinate. The model 2d of pair 2c shows that the model has 8 contact points and one possible movement. Overdeterminity of this pair is (8+1)--(5+1) = 3. Designers often choose the overdeterminate solution because of their high stiffness. The assembly of those pairs and their tolerantional treatment to remove assembly problems. After this treatment we can consider that pairs is statical determinate and have d=6. After over given treatment we can consider every pair statically determinate. We must not draw their ball models when we know that the number of contact points in the treated pair we can consider as follows:

ball joint: k = 3, rotational--translational pair: k = 4, rotational, translational, screw pairs: k = 5, unmovable pair (Abbeho principle): k = 6.

3. MECHANICAL STRUCTURES

The reasons of difficulties in assembly can not be only overdeterminate pairs but the statically overdeterminity of the whole structure. We suppose that in the structure there are tolerantionaly treated pairs, which we can consider determinate. An important factor in considering if the given structure will be assembled easy or with problems is the number of grades of freedom of analyzed structure. Till known Grubler equation gives false results.

(Valentovie, 2000) derived the question: I = (6n-6)--Ok-Or (2)

Where are:

i--number of grades of freedom, n--number of members, [SIGMA]k--sum of all contact points in the ball model of structure (the pairs are after treatment statically determinate),

[SIGMA]r--sum of members with "own" rotation, which does not influence the statically situation of the structure (member no. 3--fig. 4b).

Structures having: i [greater than or equal to] 0 are assembled without problems. The others must be dimensionally and tolerantionaly treated according to OMA methodology. Structure on the fig. 4a is overdeterminate. When we wish ourselves this structure to be unmovable and statically determinate we must take from the model of the structure 3 points, e.g. by changing three rotational pairs to rotational-translational pairs. Then will be i = 0.

[FIGURE 4 OMITTED]

4. THE EVALUATIONS OF THE RESULTS OF THE RECONSTRUCTION OF PRODUCT

OMA use for evaluation only values of the three criteria:

1. Technical complicity of assembly (Z) fig. 5,

2. Work--consumption of (P) fig. 5,

3. The grade of intelligence of assembly task.

We can imagine ourselves that the product is assembled on a machine having only orthogonal movements. Every movement has its own translational or rotational actuator. Assembled parts are not oriented and there are near to assembly holes. The product is placed in the position equipment, which enables to assembly only from above to below.

Technical complicity (Z) is the needed number of actuators (translators and rotators).Work consumption of assembly (P) is the sum of needed assembly paths. T is translational movements, r is orientation rotations, R are assembly and reposition rotations. We obtained four evaluation factors:

1. The sum of translational movements Tm (mm),

2. The sum of rotational movements Rm (rev.),

3. The sum of needed translational actuators At,

4. The sum of needed rotational actuators Ar.

The rotational movements we can transform to the circular movements on the points with maximal distance from the axe of rotation Cm (mm). The translational movements are in (mm).

Finally we can obtain the two criteria of evaluation of assembled product (Vaclav, 2005):

1. Technical complicity of assembly (Z): Y = At + Ar (3)

2. Work consumption of assembly (P): P = Cm + Tm (mm) (4)

[FIGURE 5 OMITTED]

5. CONCLUSION

1. OMA is alternative to the known DFA methods. Instead of using of rules and examples the new solutions are based on the laws of mathematics, and mechanics. 2. OMA is not only alternative to the known DFA methods. OMA is interested in all the processes of the assembly by using the theory of systems and laws of mechanics. The results are the formulations of the content of Science of Assembly. OMA determinates the structure of new science and describes the main goals in Assembly.

ACKNOWLEDGEMENTS: This paper was elaborated in the frame of project: VEGA e. 1/3163/06.

6. REFERENCES

Valentovie, E. (2000), Geometric and static condition of assembly. Assembly Automation, Vol., 20. No., 2, 2000, pp.233-236, ISSN 0144-5154

Vaclav, S. (2005), Objective Method for Assembly, Thesis. STU Faculty of Material Sciences and Technology. Department of Machining and Assembly, Trnava 2005.pp. 1-164

Valentovie, E. (1996), Knowing your orientation. Assembly Automation, Vol. 16 No. 2, Number 2, 1996, pp.31-33, ISSN 0144-5154

Mares, A. & K. Senderska (2005). Modernization of manual assembly workstation. In: 5th. International conference Research and development in mechanical industry RADMI 2005. Vrnjaeka Banja, pp. 188--191. ISBN 86-83803-20-1