Model of selective assembly of two elements with dependence of the output parameter as a quotient of the input parameters

The technological process of single-parameter selective assembly of two elements with parameters that are random variables, the values of which are determined by the finishing operations of the manufacturing processes, is considered. It is considered that the dependence between input and output parameters is nonlinear (nonlinear input-output models) and is represented in the form of quotient, and the completing rule is elementary. For a dependence of this type, expressions linking the values of tolerances (including group tolerances), limit deviations and limit values of input and output parameters are given. A method is proposed that helps to calculate group tolerances to fulfil the requirements to the accuracy of the output parameter in the whole area of its permissible values, as well as to determine the boundaries of selective groups. It is based on an iterative procedure, with each iteration consisting of sequentially executed steps. The output data of the previous iteration are the initial data for the next one. As a criterion for the end of the procedure, a given level of accuracy in calculating the average group tolerances is taken. The analytical and probabilistic model is developed, which takes into account the calculated boundaries of selective groups and helps to determine the most important indicators of selective assembly, such as the probability of formation of assembly sets, probabilities of formation of incomplete elements. An example of modelling is given, in which process indicators are determined using the developed method and model with given initial data. Prospects for further research are outlined.

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