Axis Straightness Error Evaluation of Deep Hole by Least Square Method

Precision deep hole parts are widely used in industrial productions. Axis straightness error of deep hole parts is the diameter of the smallest cylindrical surface of all the measured points, which affects a series of important parameters. The axis of the hole parts is a spatial straight line. It is difficult to evaluate the axis straightness error of deep hole parts. For the low accuracy of the axis straightness evaluation with three-dimensional coordinates, an effective and accurate evaluation method for axis straightness error of deep hole parts was proposed. The mathematical model of axis straightness error of hole parts was established by the least square method based on the center of the measurement point set. Based on the least square lines, the point set was projected to the plane which is perpendicular to the least square line. So that the spatial problem is transformed into a plane problem and the axis straightness error was changed into the diameter of the minimum circumscribed circle. The Particle swarm optimization algorithm was used to solving the diameter of the minimum circumscribed circle. Then the diameter of the least square axis containment surface was obtained. Compared with other methods, this method can evaluate the axis straightness error of hole parts effectively and accurately.