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

Jianpu Xi,Qing Yang,Cong Zhang,Laibang Zhang,Bin Li,Zexiang Zhao,Yuanchang Liu

doi:10.1155/2021/6640299

Jianpu Xi, Qing Yang + Show 5 more

Open Access

https://doi.org/10.1155/2021/6640299

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Abstract

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%.

Highlights

Scientific and technological development has resulted in aspheric optical components being utilized widely, as large and medium optical aspheric surfaces play an increasingly important role in various types of instruments and equipment including astronomical telescopes, laser fusion devices, interferometers, lenses in lithography, and other apparatus
Lee et al used the Form Talysurf system to modify the computerised numerical control (CNC) machine tool code that generated the ultraprecision single-point diamond turning machine tool path and effectively compensated for the residual form error caused by decentralising the tool during the ultraprecision machining process [4]
Based on the analysis of aspheric lens array, a Mathematical Problems in Engineering method for generating diamond forming track based on tool radius compensation in the three-dimensional path is proposed

Summary

Introduction

Scientific and technological development has resulted in aspheric optical components being utilized widely, as large and medium optical aspheric surfaces play an increasingly important role in various types of instruments and equipment including astronomical telescopes, laser fusion devices, interferometers, lenses in lithography, and other apparatus. Comley proposed parallel grinding for large-diameter aspheric off-axis aspheric surfaces and used a box structure to grind the inclined cup wheel of the machine tool to achieve XZ plane and θ axis interpolation grinding that resulted in high-precision lenses [15]. According to practical project requirements, this study proposes a NURBS interpolation method for off-axis aspheric grinding that is based on the grinding wheel path planning. E path planning scheme reduces the number of control points on the processing path, improves the processing efficiency and accuracy, and verifies the rationality and practicability of the interpolation algorithm It provides a reliable and effective theoretical basis and path optimization scheme for grinding nonspherical mirror parts

Path Planning for Off-Axis Aspheric Grinding

Optimizing the NURBS Curve Machining Path

Findings

Conclusions