An Optimization Strategy for Maximizing Coordinate Measuring Machine Productivity, Part 2: Problem Formulation, Solution, and Experimental Results

Abstract

In this, the second of two papers focused on optimizing CMM productivity, a strategy is presented for obtaining operating speeds that maximize CMM throughput. The strategy involves posing the objective and constraints in terms of a nonlinear programming problem. The objective is to minimize measuring time, and constraints are on measurement quality, available motor power and other machine specific characteristics. Solutions to various measurement scenarios are given, computed with a generalized conjugate gradient method that uses a golden section acceptable search method. Also, a sensitivity study is presented that utilizes the optimization strategy to determine how change to a CMM’s design will affect overall productivity. In the final section, experimental results utilizing the optimally computed trajectories for both single axis and multiple axis motion are given. In addition, an example is presented to demonstrate the implementation of the optimization strategy in an actual measuring application. In the example, a connecting-rod is measured at three speeds: the machine’s default speed, a speed constrained by available motor power, and the optimized speed (constrained additionally by measurement quality). The experiment demonstrates a 27 percent reduction in time for the optimized speed compared to the default speed using the Bartlett test for comparing variances in the dimensional data obtained.