Nonuniform Rational Basis Spline Interpolation for Off-Axis Aspheric Mirror Grinding Based on Wheel Path Planning

• Main Authors: Jianpu Xi, Laibang Zhang, Qing Yang, Bin Li, Zexiang Zhao, Cong Zhang
• Format: Article
• Language: English
• Published: Hindawi Limited 2021-01-01
• Series: Mathematical Problems in Engineering
• Online Access: http://dx.doi.org/10.1155/2021/6640299

Large-diameter aspheric mirrors made of hard and brittle materials suffer from low efficiency in the grinding stage, making them difficult to process. In this study, a nonuniform rational basis spline (NURBS) interpolation method is proposed and developed based on the grinding wheel path planning. The characteristic parameters of NURBS machining program are calculated to ensure the accuracy of curve interpolation path planning, and a series of control points are selected according to the normal vector points of the grinding wheel path. The control points were determined by the distance between the aspheric tangent and the next type value point at a fixed distance d. We then established a mathematical model for the knot point and simulated the relationship between the knot point and d. This indicated that d must be optimized according to the number of points to reduce the number of control points. According to this established model, a comparison experiment was conducted using an off-axis aspheric mirror, with a 280 mm diameter. Straight line and NURBS grinding were compared, and the NURBS interpolation method was shown to effectively improve grinding accuracy and efficiency by about 30%.