Mechatronic product proporcionality and inter-changeability management: mechanical components.

Zgodavova, Kristina ; Majerik, Marian

1. INTRODUCTION

It's hard to find a product today that doesn't have a chip, electronics, or some software in it. Even an ordinary, average-knowledgeable user of an industrial or any other product is able on his or her usual observation to speak meaningfully about: its technical solution; the suitability of materials used; the level of workmanship, precision of assembly operations and surface finish; the standard of service rendition.

When three assessment levels are selected, such as: better, average, and worse, [3.sup.4] = 81 different assessment statements can be pronounced out of which only one contains the better level in all four characteristics. Other statements include some quality disproportions that bring suggestions for improvement.

In the use of a product it is possible to observe more thoroughly the functionality and utility of single components, while the user may easily recognize some disproportions in utility of functions or qualities of these components

The solution to this problem falls on the shoulders of the quality managers of cooperating organisations and it is considered a serious element of their competence. As Hamel & Prahalat (1994) defined a core competence as "... a bundle of skills and technologies that enables a company to provide a particular benefit to customers". The issues of quality of mechanical components and final mechatronical products will be dealt with in such terms so that they would fit within the area of quality management system and data management system (Popovic & Vlacic, 1999) of co-operating organisations, and detailed engineering considerations will be avoided.

The aim of research described in this article was to find a relatively comprehensive set of knowledge about the need and possibilities for quality assurance of proportionality of mechanical components and modules and their interchangeability with respect to the ability of production processes cooperating organizations (Chen et al., 2009). Limit of the research was competence of the quality managers of organizations cooperating on the design parameters and tolerances of mechanical components.

2. METHODOLOGY

Quality proportionality of mechanical components is understood as a conventionally expressed mutual technical and economic balance of proportions of their standards of quality and cost of production in the quality standard and cost of production of the final mechatronical product.

The concept of 'quality proportionality' is not frequently used; nevertheless, in the system of processes forming system design, parameter design, and tolerance design (Taguchi, 1986), the fulfilment of this requirement through the loss function occurs to some extent. The same reason applies to the inevitability of taking into consideration the inter-changeability of components of final mechatronical products in the quality management of co-operating organisations. For our purposes, 'inter-changeability' can be defined as the capability of independently manufactured components to perform their effectiveness functions in the way that the effectiveness functions of final mechatronical products remain within the specified tolerances. The indicator of inter-changeability is the probability of this achievement.

When the probability equals 1, we can speak about the total inter-changeability. When the probability is lower than 1, it is a case of non-total inter-changeability. Strictly taken, it is practically impossible to reach total inter-changeability, as we can never be totally certain of any reality; however, it is possible to specify non-total inter-changeability in a particular case with such level of probability that can be regarded as corresponding to total inter-changeability. For instance, for tolerance limits at a distance of 4 standard deviations from the mean, the probability of their maintenance is 0.99994, i.e. only 6 out of 100,000 cases will fall outside the limits. In view of our methodology of investigation of quality proportionality and inter-changeability, this brings the possibility of applying two different methods: a max-min method that counts with the occurrence of values on tolerance limits or a statistical method that takes into account a particular, usually a normal distribution of values within the tolerance limits.

If the quality characteristics of a final product R can be expressed as

R = F ([P.sub.1], [P.sub.2], ... [P.sub.n]) (1)

where [P.sub.1], [P.sub.2] ..., [P.sub.n] are partial quality characteristics of product components, the mean values m shall be also governed by the function F, thus

[[mu].sub.R] = F ([[mu].sub.P1], [[mu].sub.P2], ... [[mu].sub.Pn]) (2)

and for standard deviations [sigma] is

[[sigma].sub.R] = [square root of [n.summation over (i=1)] [([partial derivative]F / [partial derivative] [P.sub.i]).sup.2] [[sigma].sub.i].sup.2] (3)

In order to avoid extensive mathematical records and derivations, we will deal neither with nominal values R, Pi nor with mean values [[mu].sub.R]. We will work only with tolerances T as the differences of specified limit values of characteristics R and Pi (1, 2, ... n). In accordance with the min-max method, it is possible to write for tolerances of quality characteristics of final mechanical conmoments [T.sub.R] and their sub-components Pi (i = 1, 2, ..., n) and for the total inter-changeability:

[T.sub.R] = [n.summation over (i=1)] [absolute value of [partial derivative]F/[partial derivative] [P.sub.i]]. [T.sub.i] (4)

The formula for tolerances with the non-total interchangeability will be built on the basis of the formula (3) using the indicator of process capability [C.sub.p]

[C.sub.p] = T / 6 [sigma] (5)

After the substitution of into (3) and its modification, we receive a new formula

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

that can be applied only when the values Pi (i=1, 2, ... n) are not correlated. The lowest tolerance value of the final product characteristic [T.sub.R] will be obtained provided that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

The formula (7) can be understood as the technical criterion of quality proportionality of final mechanical components if these are given by their tolerances. Hence, it is possible to link quality proportionality and components inter-changeability with process capability by means of the formula (6). An example of variant solutions of the quality characteristics of components and final products is given in Tab. 1.

From the management point of view it is important to incorporate the activities leading towards the appropriate application of such conception of quality proportionality and mechanical components inter-changeability and their impacts on the process capability into the quality management system of co-operating organisations. If co-operating organisations has created and adopted the quality management system based on a real or virtual quality management office (Soderlund, 2000), it is desirable to specify a set of activities within such a system focused on quality proportionality issues and mechanical components inter-changeability, as well as process capability.

[FIGURE 1 OMITTED]

3. CONCLUSION

It is necessary to regard quality management proportionality and inter-changeability of mechanical components, as well as the capability of production processes as key competence factors of quality managers in cooperating organisations. The primary task and the goal in quality management is the determination and practical fulfilment of such specification of final quality values and tolerances of product components that comply with the requirements specified for quality characteristics of final mechatronical products and take into account the potential of processes capabilities of co-operating organisations. The issues of quality proportionality and inter-changeability of mechatronicsl product components can be resolved on the basis of statistic calculations with tolerances including process capability indicators and counting with the possibilities of selective assembly or an appropriate compensation of component deviations in the assembly of final mechanical components.

4. REFERENCES

Chen, K.; Bankston, J; Panchal, J.H. & Schaefer, D. (2009). Collaborative Design and Planning for Digital Manufacturing, Springer London, ISBN 978-1-84882-2863, London

Popovic, D. (1999). Conceptual design, In: Mechatronics in Engineering Design and Product Development, Popovic, D., Vlacic, L., (Ed.), pp 274--300, Marcel Dekker, Inc., ISBN 0-8247-0226-3, New York

Prahalad, C. K. & Hamel, G. (1990). The core competences of the corporation. Harvard Business Review, Vol. 68 No.3, pp 79-91, ISSN 0017-8012

Soderlund, A. (2000). Product and Network Design--The Case of Junet, Proceedings of 1st International Conference on Cooperation & Competition, Zineldin, M. (Ed.), University of Vaxjo, Sweden, November, 2000, University of Vaxjo, Vaxjo

Taguchi, G. (1986). Introduction to Quality Engineering, Designing Quality into Product and Process, Asian Productivity Organisations, ISBN 9-2833-1083-7, Tokyo

Tab. 1. Alternatives of quality proportionality solutions--mechanical
component tolerances, inter-changeability and process capability
indicators

[P.sub.i] Hole [P.sub.2] Shaft
grinding grinding
[phi] +0.040 [phi] -0.020
+0.000 mm -0.050 mm

TOTAL INTER-CHANGEABILITY (1)

[T.sub.1] = 40 [micro]m [T.sub.2]= 30[micro]m

NON-TOTAL INTER-CHANGEABILITY (1)

[T.sub.1] = 40 [micro]m [T.sub.2] = 30 [micro]m
[C.sub.P1] = 1.33 [micro]m [C.sub.P2] = 1.33
[[sigma].sub.1] = 5 [micro]m [[sigma].sub.2] = 5 [micro]m

NON-TOTAL INTER-CHANGEABILITY (2)

[T.sub.1] = 40 [micro]m [T.sub.2] = 30 [micro]m
[C.sub.P1] = 1.33 [micro]m [C.sub.P1] = 1.33 [micro]m
[[sigma].sub.1] = 5 [micro]m [[sigma].sub.1] = 3.75 [micro]m

NON-TOTAL INTER-CHANGEABILITY (3)

[T.sub.1] = 40 [micro]m [T.sub.2] = 50 [micro]m
[C.sub.P1] = 1.33 [micro]m [C.sub.P1] = 1.33 [micro]m
[[sigma].sub.1] = 6.25 [micro]m [[sigma].sub.1] = 6.25 [micro]m

[P.sub.n]
Assembly
[phi] +0.090
+0.020 mm

TOTAL INTER-CHANGEABILITY (1)

[T.sub.R]= 70 [micro]m

NON-TOTAL INTER-CHANGEABILITY (1)

[T.sub.1] = 70 [micro]m
[C.sub.PR] = 1.90 [micro]m
[[sigma].sub.R] = 6.25 [micro]m

NON-TOTAL INTER-CHANGEABILITY (2)

[T.sub.1] = 50 [micro]m
[C.sub.P1] = 1.33 [micro]m
[[sigma].sub.1] = 6.25 [micro]m

NON-TOTAL INTER-CHANGEABILITY (3)

[T.sub.1] = 70 [micro]m
[C.sub.P1] = 1.33 [micro]m
[[sigma].sub.1] = 8.84 [micro]m