# Development of Optimal Size Range of Modules for Driving of Automatic Sliding Doors
## 1 Introduction
This typology is widespread and is used both for entrance doors and for interior doors. The guidance of the wings is by steel rollers rolling on a rail in the lower part of the frame. In its upper part, the wing is supported by the geometry of the frame, which functionally prevents it from tipping over and assists in guidance. The object is particularly suitable for size range optimization, as it is characterized by a relatively high cost and increasing demand. As a base variant for constructing the optimal size range, the basic size of a module for driving automatic sliding doors developed in [10] is used, shown in Figure 2. The module is installed in the door frame (Figure 1). It includes a toothed belt mechanism driven by a stepper motor, without a transmission mechanism (direct drive). The motor is connected to the mechanism by a self-adjusting clutch (coupling), and the end positions of the wing are determined by a need contact. The belt is fixed at both ends of the driven wing by means of special brackets. Despite the fact that a significant part of the products in the machine building, tool-making, electronic, electrical, automotive, aviation, military, construction, textile, footwear, furniture, food industries, etc., are produced in discrete sets of sizes--i.e., size ranges [5; 8; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20]--relatively few studies have been devoted to the problem of choosing an optimal size range. The number of specialists dealing with this problem who publish results of their work is also limited. This can be partly explained by the complexity of the problem and the absence of a unified approach to its solution, resulting from the great diversity of products and the functions they perform; the variety of parameters and influencing factors,; restrictions on the applicability of products, etc. ; the presence of a number of problems and unclear issues related to determining demand; the choice of objective functions and constraints when building mathematical models; the need to adapt and improve known optimization methods; etc. In addition, developments for the design and selection of an optimal size range represent \"know how\" for companies engaged in such activities, and research units specializing in this area strive to sell the achieved results as special developments to interested manufacturers at a high price. Figure 2: Basic size of a module for driving automatic sliding doors with component designations: 1—Left bearing support; 2—Toothed belt; 3—Driving pulley; 4—Right bearing support; 5—Toothed belt attachment clamps; 6—Coupling; 7—Stepper motor. Publications on the topic of size range optimization of technical products mainly consider either overly general or individual special cases and issues, which makes their application difficult. In the well-known works [5; 7; 8; 17; 18; 19; 21; 22; 23; 24; 25], some unsolved problems are also found, which can be summarized as follows:  
* There is no analysis of the problem of choosing an optimal size range, as a result of which the characteristic features that must be taken into account when solving it are determined. * In a significant part of the publications, mathematical models are presented for solving mainly single-parameter problems. The use of multi-parameter models in practice is limited. This leads to the use of simplified models that do not adequately describe the real problem and, as a consequence, a decrease in the quality of the selected solutions and the need for additional costs for adjustment and corrections in their implementation, based on the intuition, experience and professional knowledge of the designer. * Another problem is related to the insufficiently justified choice of the optimality criterion. As such, the total costs with various components included are most often used.