Abstract
The paper deals with a problem of robust optimization of mechanical assemblies, which combines the allocation of tolerances with the selection of dimensional parameters. The two tasks are carried out together with the aim of minimizing the manufacturing cost and the variation on an assembly-level functional characteristic. The problem is addressed in the specific context of planar linkages used in structures and mechanisms. The proposed solution is based on an optimality condition involving both tolerances and dimensions, which allows to define a joint optimization problem avoiding the need of two sequential optimization phases. The condition is developed with the method of Lagrange multipliers using an expanded formulation of the reciprocal power cost-tolerance function. The optimal tolerances depend on the stackup coefficients of the output characteristic, which are calculated with a tolerance analysis method based on a static analogy. The procedure is demonstrated on two examples to illustrate some application details and discuss potential advantages and limitations.
Highlights
The parts of a mechanical assembly are manufactured with random deviations from their nominal geometry
The proposed method treats the dimensions as direct optimization variables, while the tolerances are set in background using conditions for optimal allocation. These are found using an analytical optimization method (Lagrange multipliers), a cost-tolerance function including the effect of dimensions, and a method for stackup analysis based on a static analogy
The core of Taguchi methods is parameter design, which uses an experimental plan based on orthogonal arrays to select the settings of system inputs that are less sensitive to noise factors
Summary
The parts of a mechanical assembly are manufactured with random deviations from their nominal geometry. The error stackup depends on the nominal dimensions of the features as well In principle, these could be optimized together with the tolerances, so that the specified assembly variation could be met with wider tolerances on the individual parts. Int J Adv Manuf Technol (2020) 111:3141–3157 allocation problem would make sense for any type of assembly, the study will focus on planar linkages for applications in structures and mechanisms These are interesting for tolerancing problems as their complex layout may involve some difficulties in stackup calculations; they lend themselves to a simple, standard definition of the optimization problem. The proposed method treats the dimensions as direct optimization variables, while the tolerances are set in background using conditions for optimal allocation These are found using an analytical optimization method (Lagrange multipliers), a cost-tolerance function including the effect of dimensions, and a method for stackup analysis based on a static analogy.
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