Determination of the parameters of typical multi-link dimensional chains (closing link is tension) using recurrent dependencies

¹ Izhevsk State Technical University, 7, Studencheskaya street, Izhevsk, 426069, Russia
² Penza State University, 40, Krasnaya street, Penza, 440026, Russia
³ Perm State Agro-Technological University, 23, Petropavlovskaia street, Perm, 614990, Russia

^* Corresponding author: shiljaev@mail.ru

Abstract

The existing approach to the use of the group interchangeability method during assembly, which are concentrated, has a number of significant drawbacks: 1) there are no formulas for calculating the upper and lower deviations of the component parts of the dimensional chain; 2) deviations are selected without taking into account the design of the component links (the method of equal tolerances is used); 3) the method is applicable for the number of links no more than three with a small number of groups. For other types of problems there is no algorithm, mathematical apparatus, and examples of calculation are not considered sequentially; 4) the calculation by the group interchangeability method is limited by the condition of equal tolerances, i.e. excluding compensators and compensating properties of materials as a part of mechanisms; 5) the calculations are based on assumptions about the economic feasibility of increasing the closing link by a factor of n without taking into account the feasibility of such an increase in the component links that is not permissible in complex mechanisms; 6) the size of the batch of parts and the volume of work in progress are not reflected, as one of the factors of economic feasibility of establishing production tolerance. In this regard, it is necessary to improve the method of achieving accuracy by group interchangeability. This article discusses typical problems that rise when solving dimensional chains in which the closing link is a tension.