Tolerance Synthesis for Nonlinear Systems Based on Nonlinear Programming

Automatic assignment of tolerances to dimensioned mechanical assemblies is studied as an optimization problem; the objective of which is to minimize the (manufacturing) cost, subject to the constraints of (design) functionality and (assembly) interchange-ability. By associating a nominal dimension and a tolerance to the variance, a probabilistic approach is adopted. Trigonometric functions relating the component geometries give rise to the nonlinearity in the system. Estimating an n-dimensional nonlinear integral by a polytope converts the probabilistic optimization formulation to a deterministic one. It also allows rapid evaluation of tolerance analysis embedded in tolerance synthesis. Local optimality is ensured by analysis of convexity and quasi-concavity of the objective function and some of the constraints. Sensitivity analysis is performed to provide search directions for global optimality. An implementation is reported with an example.