UDC 621.01.11

MECHANICS

Academician I. I. ARTOBOLEVSKY, D. Ya. ILYINSKY, I. I. KAPUSTIN

SYNTHESIS OF AUTOMATIC MACHINES AND THEIR PRODUCTIVITY

The classification of developed mechanisms carried out in work (¹), proceeding from their functional purpose in an automatic machine, may be developed in the following form.

I. Functional units (“indivisible” developed mechanisms intended for processing material and energy flows).

1) Working units (working heads and auto-operators performing the actual working operations).

2) Feeding and positioning units, ensuring specified relative positions of the products being processed and of the working units, and their displacements according to prescribed laws along one, two, or three coordinates.

3) Transport units, carrying out movement from position to position, transfer, etc.

II. Functional systems (complex developed mechanisms intended for processing material, energy, and information flows).

1) Automatic-control systems (including inspection, regulation, interlocking, actual counting and weighing, etc.).

2) Systems for automatic feeding with initial materials.

3) Systems for automation of auxiliary functions of a “sectoral” character (clamping—unclamping and fixation of blanks in metalworking, opening—closing of press molds in molding products from plastics and rubber, thread trimming in sewing-machine construction, etc.) and of a “general” character (lubrication, etc.).

In mechanical engineering, the problem of design has been most fully developed at the level of synthesis of elementary mechanisms, the methods of which, constituting the principal content of the theory of mechanisms, are the foundation of the whole mechanics of machines. Far less complete and comprehensive is the theory of synthesis of functional mechanisms; in developing its foundations, the broad possibilities of interbranch unification both of the mechanisms themselves and of the methods of their design are not always considered. The principles and methods for the synthesis of elementary mechanisms are in many respects applicable to solving problems of synthesis not only of the functional elements of automatic machines, but also of automatic machines themselves as a whole. Being directly connected with production, the synthesis of automatic machines, characterized by the exceptionally great complexity and multistage nature of the problems to be solved and by close links with the techno-economic aspects of problems and the rational use of new technology, constitutes one of the most rapidly developing branches of the general theory of machines. The development of the problem of synthesis of automatic machines is based on the successes of the theory of productivity and reliability of machines, the achievements of operations research theory and general systems theory, as well as on the development of aggregate principles of machine construction.

As the most generalized and objective criterion for evaluating (objective function of) the quality of automatic machines, it is expedient to use such an indicator as the productivity of social labor, the cost of production, etc.

With the growth of the level of synthesis of mechanisms, the task of choosing the objective function becomes more complicated, and the number of factors determining the целе-

function, the interrelations among these factors become more complicated; in addition to analytical dependences, non-analytical ones arise; alongside deterministic dependences, complex stochastic dependences appear; groups of factors emerge that are characterized by a competing influence on the objective function, which, among other things, may be discontinuous, nonlinear, nondifferentiable, etc.

The problem of designing an automatic machine must be solved on the basis of: 1) optimization of its basic parameters, i.e., obtaining values of the objective function that are, as far as possible, closer to the maximum (minimum); 2) finding the specified parameters in the zone of admissible values, determined by the initial boundary conditions; 3) satisfying the specified conditions relating to convenience and safety of operation, etc.

Since the interrelated indicators of productivity and reliability of machines are among the principal technical-and-economic characteristics, we shall set forth the basic propositions of the theory of productivity, proceeding from the problems of synthesis of mechanisms and machines and using the numerous data on the analysis and forecasting of machine productivity in various branches of industry \((^{2-6})\).

The actual productivity of a machine, representing the number of standard units of product obtained (processed, assembled, etc.) per unit time on the given machine, is

\[ Q_{\mathrm{f}} = \frac{m}{T_{\mathrm{p}}}\eta_{\mathrm{is}}, \]

where \(T_{\mathrm{p}}\) is the duration of the working cycle, i.e., the time corresponding to the output of one unit of product; \(m\) is the dimensionality coefficient; \(\eta_{\mathrm{is}}\) is the overall utilization coefficient.

The technological cycle of a machine \(T_{\mathrm{t}}\) is composed of the time expenditures \(\sum t_{\mathrm{p}}\), during which all actual working operations for obtaining a unit of product are performed, and the cyclic time losses \(\sum t_{\mathrm{pc}}\) due to auxiliary cyclic operations that are not combined in time but are directly associated with the actual working cyclic operations (i.e., accompanying the production of each unit of product). Thus,

\[ T_{\mathrm{t}} = \sum t_{\mathrm{p}} + \sum t_{\mathrm{pc}}. \]

The relations between the duration of the working cycle \(T_{\mathrm{p}}\) and the technological cycle \(T_{\mathrm{t}}\) for various types and classes of machines are given in works \((^{2,3})\).

The values of the dimensionality coefficient \(m\) are given in Table 1.

Table 1

The machine utilization coefficient \(\eta_{\mathrm{ис}}\), characterizing the magnitude of noncycle (i.e., not directly connected with the actual working operations and accompanying the obtaining of several units of product) time expenditures (losses)

\[ \sum_{i=1}^{\varepsilon}\sum t_{\mathrm{пв}} \]

is

\[ \eta_{\mathrm{ис}}= \left[\sum_{i=1}^{\varepsilon}\frac{1}{\eta_{\mathrm{ис}\,i}}-(\varepsilon-1)\right]^{-1} = \left[1+\sum_{i=1}^{\varepsilon}\frac{1-\eta_{\mathrm{ис}\,i}}{\eta_{\mathrm{ис}\,i}}\right]^{-1}, \]

where \(\eta_{\mathrm{ис}\,i}\) are partial utilization coefficients characterizing the noncycle time losses of the \(i\)-th kind referred to a unit of output (i.e., \(\sum t_{\mathrm{пв}\,i}\)) and written in general form, respectively, as

\[ \eta_{\mathrm{ис}\,i}=\left[1+\frac{\sum t_{\mathrm{пв}\,i}}{T_{\mathrm{р}}}\right]^{-1}; \]

\(\varepsilon\) is the total number of partial utilization coefficients (i.e., “items” of noncycle time expenditures into which, in the given case, all noncycle losses are subdivided).

Table 2

Noncycle time losses and the corresponding partial utilization coefficients

The noncycle time losses consist of nonrandom (regulated, periodic, of predetermined duration) downtimes and random downtimes of the machine, the frequency and duration of which are probabilistic in character, since they are caused chiefly by the unreliability of the means of production (i.e., the unreliability of the machine’s own mechanisms and the nonconditioned state of the initial materials) (Table 2). Other kinds of noncycle losses may be taken into account in determining the coefficient of operating regime and the actual duration of the shift.

The overall utilization coefficient is

\[ \frac{1}{\eta_{\mathrm{ис}}} = \underbrace{ \frac{1}{\eta_{\mathrm{ин}}} + \frac{1}{\eta_{\mathrm{рем}}} + \frac{1}{\eta_{\mathrm{пит}}} + \frac{1}{\eta_{\mathrm{обсл}}} }_{\text{nonrandom losses}} + \underbrace{ \frac{1}{\eta_{\mathrm{над}}} + \frac{1}{\eta_{\mathrm{мат}}} }_{\text{random losses}} -5 \]

The partial utilization coefficient characterizing the reliability of the machine itself and, as a consequence, often called the reliability coefficient (sometimes the availability coefficient), is determined by the equation

\[ \eta_{\mathrm{над}}= \left[1+\frac{\sum t_{\mathrm{пв\,над}}}{T_{\mathrm{р}}}\right]^{-1} = \]

\[ = \left[ 1 + \sum_{i=1}^{n} \frac{m_i T_{\mathrm{B}i}}{T_i} \right]^{-1} = \left[ 1 + \sum_{i=1}^{n} m_i B_i \right]^{-1} = [1 + B_{\mathrm{общ}}]^{-1}, \]

where \(T_{\mathrm{B}i}\) and \(T_i\) are, respectively, the mean restoration time and the mean time between failures of the \(i\)-th functional mechanism or device of the machine;

\[ B_i = \frac{T_{\mathrm{B}i}}{T_i} \quad \text{and} \quad \sum_{i=1}^{n} \frac{m_i T_{\mathrm{B}i}}{T_i} = B_{\mathrm{общ}} \]

are the specific (per unit time) duration of adjustment\({}^{4}\), respectively, of the \(i\)-th functional mechanism or device and of the entire machine; \(m_i\) is the number of identical specimens of the \(i\)-th standard size or type of functional mechanism (or device), the total number of standard sizes or types of which in the given machine is \(n\).

The partial utilization coefficient that estimates noncyclic losses of time due to substandard quality of the raw materials (this indicator is of especially great importance for assembly automata) is

\[ \eta_{\mathrm{мат}} = \left[ 1 + \frac{t_{\mathrm{пв.мат}}}{T_{\mathrm{p}}} \right]^{-1} = \left[ 1 + \frac{T_{\mathrm{Вм}}}{T_{\mathrm{p}}} P_{\mathrm{м}} P_{0} q \right]^{-1} = [1 + q B_{\mathrm{м}}]^{-1}; \]

where \(T_{\mathrm{Вм}}\) is the mean time for restoring the operability of the machine, the loss of which was caused by the arrival of a unit of substandard raw material (one part, blank, etc.); \(P_{\mathrm{м}}\) is an indicator of the quality of the raw materials: the probability that substandard materials (parts) will occur among the total mass of supplied materials (parts); \(P_0\) is an indicator of the machine’s “sensitivity” to the quality of the raw materials: the probability of finding, among the entire mass of substandard materials, units of material (parts) with such signs of substandard quality (defects, etc.) as cause stoppage of the machine \((0 < P_0 \leqslant 1)\); \(q\) is the number of streams of materials (parts) simultaneously fed into the machine; \(B_{\mathrm{м}} = \dfrac{T_{\mathrm{Вм}}}{T_{\mathrm{p}}} P_{\mathrm{м}} P_0\) is the specific (per unit time) duration of adjustment of the machine when it is stopped because of the arrival of a unit of substandard raw material.

Having established how the quality of the mechanisms entering into an automatic machine (which, as is known, is largely determined by reliability and, consequently, by their principle of operation), the number of these mechanisms, and also the quality of the raw materials affect productivity, we obtain the possibility of linking the problems of synthesizing an automatic machine with predictive calculations of techno-economic characteristics and with the search for optimal variants of newly created and modernized machines and lines.

State Scientific-Research Institute of Machine Science

All-Union Correspondence Institute
of the Textile and Light Industry

Received
29 XI 1968

CITED LITERATURE

\({}^{1}\) I. I. Artobolevsky, Theory of Mechanisms, Moscow, 1965.
\({}^{2}\) S. I. Artobolevsky, Technological Automatic Machines, Moscow, 1964.
\({}^{3}\) P. I. Burov, I. I. Kapustin, Calculation of the Productivity of Working Machines, Moscow, 1958.
\({}^{4}\) A. P. Vladzievsky, Automatic Lines in Machine Building, Moscow, 1958.
\({}^{5}\) L. N. Koshkin, I. A. Kutsov, et al., Automatic Lines of a Rotary Type, Tula, 1961.
\({}^{6}\) G. A. Shaumyan, L. I. Volchkevich, M. M. Kuznetsov, Automation of Production Processes, Moscow, 1967.