Two-element Selective Assembly with Non-linear Input-output Models Using Approximation

Abstract

The process of single-parameter selective assembly of two elements is considered for the case of a nonlinear input-output modelapplication. Due to the objective complexity of determining the relations between the limit deviations and tolerances of input and output parameters, as well as the relative accuracy smallness due to the precision of the assembly, it is reasonable to represent the initial model in the form of a first-order polynomial of two variables. Linearisation is proposed to be carried out using a method of obtaining an approximating relation in the form of a Taylor series and by means of a multivariate least square method, with subsequent variantcomparison according to a given criterion. The criterion for choosing one of the two proposed variants is the minimum average approximation error. To determine the values of group tolerances, it is proposed to use two methods: assigning the equal tolerances and assigning tolerances of the equal relative accuracy. For both methods the derivation of the set-making equations is given, allowing the use of selective group numbersunder certain assumptions. Using a linearized model, the main indicators of the assembly process are determined: the number of assembly sets, work in progress and preliminary scrap. An example is given for the case when the output parameter represents the product of the input elementparameters. The coefficients were calculated and the set-making equation was derived. Comparison of the results presented in the paper with earlier obtained results (initial nonlinear model) shows a relatively small divergence in calculating the boundaries of selective groups, the error in determining the probability of obtaining assembly sets as a whole does not exceed 0.5%. The proposed method is applicable in case of small values of relative accuracy of input and output parameters, which in practice corresponds to selective assembly of precision products.