Mathematical Model of Cylindrical Parts Assembly using Digital Twins

Increasing the accuracy of manufacturing and assembling products determines new requirements for mathematical models. It is necessary to move from the requirements specified by the drawing to digital twins obtained as a result of geometry measurement. Having developed digital twins of individual products, you can simulate the assembly of products and determined the location and orientation errors. This makes it possible to more effectively normalize the geometric specifications at the stage of designing units and mechanisms. In the production of products, assembly efficiency can be improved by pre-simulation. To date, several approaches have been developed for modeling the assembly of surfaces with form deviations. The article proposes a new mathematical model based on the difference plane, which is obtained by reaming the cylinders. The difference plane defines three points of contact and then the position of the axis of the movable cylinder. In accordance with the calculation data, the movable cylinder in the assembly is displaced along two axes and rotated around two axes. The main result of the calculation of the assembly will be the orientation error in the form of a parallelism tolerance and the location error in the form of a coaxiality tolerance. In an assembly with a gap, you can also calculate a variable location and orientation error as the product rotates. The simulation performed showed a high degree of adequacy of the developed mathematical model.