Research On Recognition And Assessment Of Typical Planar Curves Used In Precision Manufacturing

Through development of form measurement, the basis measurement pattern has been adopted. The geometric parameters of the measured object should be known when measuring and evaluating their form error. The set of measuring instruments are dependent on geometric parameters of the measured object.There is a problem how to measure the object of the unknown parameters and evaluate its form error in the modern manufacturing. It brings a new challenge to the traditional measurement pattern. The new measurement pattern is concerned with two main problems: control of measurement process, shape recognition and assessment of form error. The first problem has been solved by advanced technology such as Numerical Control, software engineering, precision machinery and sensors. How to solve the second problem is the key to the new measurement pattern. This dissertation will focus on the second problem and study recognition and assessment of typical planar curves used in precision manufacturing. The main research is as follows:(1) Based on the differential geometry, six algorithms for shape recognition were proposed with rotation and translation invariance and used in the planar curves. The inherent invariable of the planar curves were computed. The values of algorithm for the planar curves were extracted when their parameters were unknown and compared with the inherent invariable of the planar curves, so the planar curves were recognized.(2) Evaluation of the roundness error was studied deeply in this dissertation. The criteria of the minimum zone circle method, minimum circumscribed circle method and maximum inscribed circle method were researched and the criterion of obtuse triangle was proposed. Based on the criteria of roundness error, the definition of the circumscribed circle and inscribed circle with the least roundness error was given. The solution to the circumscribed circle and inscribed circle with the least roundness error was proposed when they met with the criterion of obtuse triangle.Evaluation of the minimum zone circle was dependent on four feature points, whereas assessment of the minimum circumscribed circle and maximum inscribed circle was determined by three or two points. The relationship between the minimum zone circle, minimum circumscribed circle and maximum inscribed circle was studied. Based on their relationship, the minimum zone circle and minimum circumscribed circle, maximum inscribed circle were transformed mutually. Thus, evaluation of the minimum zone circle could be solved effectively.Three methods of assessment of roundness error were proposed in this dissertation. Based on the criteria of the minimum zone circle, minimum circumscribed circle and maximum inscribed circle and convex hull, a unified approach was proposed to evaluate roundness error of the minimum zone circle, minimum circumscribed circle and maximum inscribed circle. Evaluation of the minimum zone circle, minimum circumscribed circle and maximum inscribed circle was fulfilled with rotation based the contact pattern. The minimum circumscribed circle and maximum inscribed circle were evaluated with curvature and the curvature circle.(3) The criterion of profile error of ellipses was studied and profile error of ellipses was evaluated according to algebraic distance.The proposed algorithms could recognize the planar curves effectively through test. The ideal model of the planar curve was established and its error was evaluated. It showed the correctness of the criteria of roundness error and relationship between the minimum zone circle, minimum circumscribed circle and maximum inscribed circle and the effectiveness of the methods for evaluation of roundness error.