ISSN 1068�798X, Russian Engineering Research, 2010, Vol. 30, No. 3, pp. 305–307. © Allerton Press, Inc., 2010.Original Russian Text © Yu.L. Chigirinskii, 2009, published in STIN, 2009, No. 12, pp. 26–29.

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The best approach to formalizing the relationbetween the machining sequence of individual sur�faces and the overall precision is dimensional analysisof industrial processes in which the specific techno�logical sequence is expressed as a system of linearequations [1]. The mathematical apparatus for thesolution of a system of equations is traditionally stud�ied in university courses on higher mathematics. Thisis not the case for the unformalized generation of asystem of equations describing the machiningsequence. If we consider the technological process as astructural–time table, we may represent the machin�ing sequence in the form of an oriented graph. The useof discrete mathematics reduces the generation of amathematical model of machining to Euler’s familiarKonigsberg’s bridge problem. Using any Euler�pathsearch algorithm in a graph, we may verify the pres�ence of relations between the boundaries of the closingelements and thus obtain a description of the graph asa system of linear equations.

A similar discussion applies when we want to deter�mine possible sequences of machining methods inproducing surfaces of specified accuracy. In this case,analysis of the machining�precision tables permits theconstruction of a surface�machining graph, in whichwe may find either Euler paths (all possible sequences)or, by specifying the length of each portion of thegraph, the shortest path (the optimal sequence). Theselection of the optimization criteria determines howeconomical this approach will be. For example, theproduction costs (time, energy, and materials) wereadopted as the criterion in [2, 3].

Other linear�programming problems include thecalculation of optimal machining conditions; the cal�culation of operational stocks; and synchronization ofindividual operations in the design of the productionflow.

Thus, technological design may be analyzed on thebasis of economic and mathematical simulation. Inparticular, technological problems may be regarded asoptimization problems. For most technological�design problems, we may find a set of correct solutions(solutions satisfying the constraints), from which weidentify the optimal solution. The basic requirementsthat the final process musty satisfy include specifiedprecision and quality of the products [4]. Any eco�nomic characteristic—such as the machining cost—

may be used in optimization (in accordance with theprior analysis of the problem) [2, 3].

Traditionally, the following sequence is recom�mended for the development of a machining process:analysis of the object to be produced; determination ofa type of production; preliminary (rough) selection ofthe equipment; selection of the initial blank; analysisof possible shaping methods for individual surfaces;development of the surface�machining sequence;refined selection of the equipment; selection of thetechnological bases; and the development of plans forindividual operations.

The machining pathway for an individual surface isdesigned on the basis of the working diagram and thecharacteristics of the chosen blank. Possible methodsof final machining may be selected from the specifiedprecision and surface roughness, if the size, mass, andshape of the blank are known [4]. The specificity of theindividual operations prevents a final conclusionregarding the machining accuracy, since there is nocomprehensive similarity between them. In particular,the dimensions and shape of the machined blanks, thestate of the machine tools, the machining conditions,and other factors are different. Although precisiontables give only a general idea of the possible machin�ing precision, they are required as reference data indesigning the technological processes [4].

For the sake of simplicity, we consider only twoparameters (Table 1): 1) the height of the microprojec�tions (roughness Ra) as a characteristic of themachined surface; 2) the quality number N as a char�acteristic of the machining precision IT. Each

Formalized Approaches in Technological DesignYu. L. Chigirinskii

Volgograd State Technical University, Volgograd

DOI: 10.3103/S1068798X10030251

Table 1

Machining method Ra, µm N

Turning Preliminary roughing 100–50 17–14

Roughing 50–25 14–12

Semifinishing 12.5–3.2 12–10

Finishing 6.3–1.6 11–7

Fine 0.8–0.4 7–6

Grinding Preliminary 1.6–0.8 8–7

Finishing 0.8–0.4 7–4

Fine 0.4–0.1 5–3

306

RUSSIAN ENGINEERING RESEARCH Vol. 30 No. 3 2010

CHIGIRINSKII

machining method corresponds to a range of qualityand precision characteristics. The limiting values inthe range are determined from economic consider�ations (the lower boundaries of the range) or by theattainability of the result on the basis of the capabilitiesof the method (the upper boundaries of the range).

For example, a surface with Ra = 1.6 μm may beobtained by final turning (upper boundary of therange), but the probability of ensuring specified sur�face quality in that case is too low. Therefore, somereduction in the machining conditions is probablyrequired, or a cutting tool with special geometry mustbe used, with unjustifiable increase in machiningcosts. At the same time, preliminary grinding (thelower boundary of the range) guarantees the requiredsurface quality with minimum machining costs.

Note, however, that the reliability of the referencedata is unsatisfactory. Research confirms the signifi�cant (up to 15–40%) difference between the data indifferent sources. This discrepancy may be attributedto differences in the specialist literature and the lowreliability of the statistical methods used in compilingthe handbooks.

The completeness of the reference data is also insuf�ficient. As a result, engineering influence allows themachining�precision tables to be supplemented byinformation regarding the potential ability of eachmachining method to boost surface quality or machin�ing precision. At present, the characteristics of machin�ing methods are determined differently at differententerprises: 1) empirically; 2) in the light of literaturerecommendations [5–7]; 3) subjectively. In all thesecases, technological errors are likely; their detectionand operation is only possible in the last stages of thetechnological preparations for production.

Consider a technological chain consisting of twooperations in sequence: rough and semifinal turning ofan external cylindrical surface. This chain produces asurface with Ra = 12.5–3.2 μm (Table 1). According tothe rules of approximate calculations [1]

or

(1)

If we compare the probable roughness values inEq. (1) (as recommended in calculations from initialreference data), we find that the height of the micro�projections at the machined surface in the last processmay be reduced by a factor of 2–16—i.e., within pre�cision classes (9 ± 7).

However, informal data obtained by separate com�parison of the upper and lower boundaries of the range

or

(2)

show that the surface quality is raised no more than(4–8)�fold—i.e., within precision classes (6 ± 2) .

Analogous discussions regarding the dimensionalprecision yield refinements by factors of 1–3—i.e.,precision classes (2 ± 1)—as against the formal valuein the range from –1 to 5—i.e., within precisionclasses (2 ± 3). However, statistical data determinedoutside the rated range must be regarded with skepti�cism. As an example, we present the modified machin�ing�precision table (Table 2).

Suppose that the problem has been solved. In otherwords, statistically reliable information regarding therise in surface quality and dimensional precision(decrease in precision class and relative reduction inmicroprojection height at the machined surface) hasbeen established and verified for each technologicalmethod. Then, we may add these data to existinghandbook data (Table 2). In that case, the possibility of

δITmin ITi

min ITi 1–max

; δITmax ITi

max ITi 1–min–=–=

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min Rai

min

Rai 1–

max���������; δRa

max Rai

max

Rai 1–

min���������.==

δITmin ITi

min ITi 1–min

; δITmax ITi

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min Rai

min

Rai 1–

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Table 2

Machining method Ra, µm Improve�ment IT Improve�

ment

Turn�ing

Roughing 50–25 2 14–12 2–3

Semifinishing 12.5–3.2 4–8 12–10 2

Grind�ing

Finishing 0.8–0.4 2–4 7–6 1–4

Fine 0.4–0.1 2–4 5–3 2–3

a 1

a21

a 2

a 4

a 5

a 31

a 41

a3

2

1

Grid model of machining: (1) blank; (2) product; for a1,a2, a3, a4, a5, a21, a31, a41, see Table 4.

RUSSIAN ENGINEERING RESEARCH Vol. 30 No. 3 2010

FORMALIZED APPROACHES IN TECHNOLOGICAL DESIGN 307

using mathematical methods for the analysis ofmachining precision is obvious.

As an example, consider a grid model for themachining pathway employed at an external cylindri�cal surface (precision IT 7; microprojection heightRa = 0.8–1.25 µm). In accordance with the precisiontables, we may propose several equivalent (in terms ofproduct quality) machining methods (Table 3).

Possible machining technologies are representedby the grid model shown in the figure, with the struc�ture in Table 4.

Note that the same machining methods in differentsequence require different implementation times. Forexample, preliminary grinding as the last step inmachining (cases 2 and 5) requires a certain time (a41)to ensure the specified product quality (Ra = 0.8–1.25 µm) and precision (IT 7). When used as an inter�mediate step, the same method is intended for roughmachining and correspondingly requires less time (a4).The same considerations apply to other technologicalmethods (semifinal and final turning) in the machiningproposals.

Depending on the projected production condi�tions—organization, scale of production, configura�tion of the equipment, economic factors (productioncycle), etc.—maintenance of the required productquality may be reduced to an optimization problem, asfollows [2, 8].

(1) Determining the flux of lowest cost or the short�est path for large�scale production with distribution ofthe equipment along the technological path.

(2) Determining the shortest path or maximumflow for production with strict productivity require�ments.

(3) Determining the maximum flux or redistribut�ing resources for medium�scale or one�off produc�tion, with grouping of the equipment.

REFERENCES

1. Shamin, V.Yu., Teoriya i praktika razmerno�tochnost�nogo proektirovaniya (Theory and Practice of Dimen�sional�Precision Design), Chelyabinsk: Izd. YuUrGU,2007.

2. Pontragin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V.,and Mishchenko, K.F., Matematicheskaya teoriya opti�mal’nykh protsessov (Mathematical Theory of OptimalProcesses), Moscow: Nauka, 1961.

3. Nikiforov, A.D., Sovremennye problemy nauki v oblastitekhnologii mashinostroeniya (Current Scientific Prob�lems in Manufacturing Technology), Moscow: Vysh�chaya Shkola, 2006.

4. Spravochnik tekhnologa mashinostroitelya (Manufactur�ing Handbook), Kosilova, A.G. and Meshcheryakov, R.K.,Ed., Moscow: Mashinostroenie, 1986, vol. 1.

5. Vasil’ev, A.S., Dal’skii, A.M., Zolotarevskii, Yu.M.,and Kolpakov, A.I., Napravlennoe formirovanie svoistvizdelii mashinostroeniya (Selecting the Properties ofManufacturing Components), Moscow: Mashinostro�enie, 2005.

6. Dal’skii, A.M., Tekhnologicheskoe obespechenienadezhnosti vysokotochnykh detalei mashin (Equipmentfor Producing Reliable High�Precision MachineParts), Moscow: Mashinostroenie, 1975.

7. Korsikov, V.S., Tochnost mekhanicheskoi obrabotki(Machining Precision), Moscow: Mashinostroenie,1975.

8. Wentzel, E.S., Issledovanie operatsii: zadachi, printsipy,metodologiya (Operations Research: A MethodologicalApproach), Moscow: Nauka, 1988.

Table 4

Machining method Expenditures Preceding element

Rough turning a1

Semifinal turning a2 a21

a1

Final turning a3

a31

a2

Preliminary grinding a4

a41

a21, a3

Final grinding a5 a4

Table 3

Machining method

1 2 3 4 5

I I I I I

II II II II II

III III IV III IV

IV IV V – –

V – – – –

Note: The notation adopted is as follows: I) rough turning; II) semifinalturning; III) final turning; IV) preliminary grinding; V) finalgrinding.