# Development of Optimal Size Range of Modules for Driving of Automatic Sliding Doors
## 1 Introduction  
Automatic sliding doors are widely used in the construction sector in the construction of residential, industrial, administrative, public, and other facilities. They are also used as a building component in modern intelligent building automation systems, which makes them promising products for production. Their wide distribution is due to a number of their characteristic features, the most important of which are high degree of reliability; long service life; minimal maintenance costs; silent operation; stylish and innovative design; high level of energy efficiency; low electricity consumption; possibility of management with mobile applications installed on smartphones, tablets, etc. ; easy passage of people with disabilities; etc. Leading manufacturers of automatic sliding doors on the European market--Dormakaba [1], Alumil [2], Record [3], GEZE [4], etc.--offer a wide variety of typologies and functions, but in general the drive system is based on one basic representative type. It is a linear motion module with an electric drive, which is sized to move the heaviest possible door wings with the required speed and stroke length. Thus, in cases where it is necessary to drive wings with a smaller mass, they are equipped with oversized modules, which leads to an increase in the overall dimensions, mass, and value of thestructurally connected building elements of the sliding doors, as well as to an increase in energy, maintenance, and repair costs. For door manufacturers, the use of only one size reduces the time and costs of design and manufacturing due to the \"training effect\" [5; 6] or the \"learning effect\" [7], but for users this leads to an increase in the price of doors and the costs of their operation, i.e., to additional costs due to the discrepancy between the products demanded by users and those offered by manufacturers. This increases the risk of losing markets for manufacturers and reduces the economic efficiency of the application. On the other hand, if for each specific case a special module is developed, then for the main parameters which are calculated to correspond exactly to the input parameters (mass and dimensions of the wings, stroke length, etc.) of the specific problem, the wide variety of possible values of the main parameters of the modules (load capacity, stroke length, speed, acceleration, etc.) will lead to a significant number of sizes. In this case, the operating costs will be reduced, because modules will be used that have parameters which meet the calculation requirements, but the design and production time and costs will increase due to the reduction in the production quantities in the batches of the manufactured products and the increase in their variety. In this case, the success of the application of the products is also questionable. One of the effective and proven ways to solve these problems is the development of a size range of modules for driving sliding doors, which is a compromise between the conflicting interests of manufacturers and consumers [5; 7; 8]. Finding it is associated with solving the following optimization problem: to determine the set of elements of a size range of modules for driving automatic sliding doors and the required number of each element, which satisfies all demand in terms of type and quantity and optimizes under given constraints a selected objective function, taking into account the costs in the field of production and operation. Solving the defined problem and finding the optimal size range will minimize the costs caused by diversity, since all elements (sizes) of one size range are based on the use of the same idea, structure, materials, and production methods [9], and will lead to an increase in the competitiveness of the manufactured products and the efficiency of their application. The object of consideration are modules for driving automatic sliding doors (Figure 1) with two movable wings that close towards the center of the clear opening. Figure 1: Drive module integrated into the door side pillars.