Trajectory planning of optical polishing based on optimized implementation of dwell time

Abstract This paper presents a study on the trajectory planning of optical polishing based on an optimized implementation of dwell time to improve the polishing quality and efficiency of optical surfaces. The large-scale, sparse, and ill-posed linear equation solution is transformed into a quadratic programming problem with boundary constraint, and the monotone projection gradient method is adopted to obtain an optimal dwell time solution by considering its fluctuation characteristic. Then, parametric polishing paths are constructed using cubic B-spline curves to guarantee one-to-one correspondence between each curve segment and dwell time of a removal spot. Finally, an interpolation process of polishing trajectory is proposed on the basis of the equal–proportional feed rate adjustment strategy to improve the implementation accuracy of dwell time. Simulation and experimental results show that the proposed dwell time algorithm and spline interpolation method can considerably improve the solution accuracy of dwell time and the convergence rate of the form error during polishing. These results provide important scientific basis and technical support for the high-efficiency and high-precision polishing of large-aperture aspheric optical surfaces.

[1]  Charles M. Egert,et al.  Advanced matrix-based algorithm for ion-beam milling of optical components , 1992, Optics & Photonics.

[2]  Luo Fuyuan,et al.  Research on the Algorithm of NURBS Curve Bidirectional Optimization Interpolation with S-type Acceleration and Deceleration Control , 2012 .

[3]  Dong Zhao,et al.  Kinematic calibration of a 6-DOF hybrid robot by considering multicollinearity in the identification Jacobian , 2019, Mechanism and Machine Theory.

[4]  Chi Fai Cheung,et al.  Model-based self-optimization method for form correction in the computer controlled bonnet polishing of optical freeform surfaces. , 2018, Optics express.

[5]  R. A. Jones,et al.  Optimization of computer controlled polishing. , 1977, Applied optics.

[6]  M. Steinbuch,et al.  Development and performance demonstration of the NANOMEFOS non-contact measurement machine for freeform optics , 2011 .

[7]  Chi Fai Cheung,et al.  Modelling and simulation of structure surface generation using computer controlled ultra-precision polishing , 2011 .

[8]  Zhichao Dong,et al.  Peano-like paths for subaperture polishing of optical aspherical surfaces. , 2013, Applied optics.

[9]  Yunqing Zhang,et al.  Manufacturing- and machining-based topology optimization , 2006 .

[10]  Suet To,et al.  An integrated form characterization method for measuring ultra-precision freeform surfaces , 2007 .

[11]  Dong Zhao,et al.  A Trajectory Planning Method for Polishing Optical Elements Based on a Non-Uniform Rational B-Spline Curve , 2018, Applied Sciences.

[12]  Xianhua Chen,et al.  Mid-Spatial Frequency Error (PSD-2) of optics induced during CCOS and full-aperture polishing , 2013 .

[13]  Liu Xinhua,et al.  A novel approach for NURBS interpolation through the integration of acc-jerk-continuous-based control method and look-ahead algorithm , 2017 .

[14]  W. T. Lei,et al.  Robust real-time NURBS path interpolators , 2009 .

[15]  Michael A. Saunders,et al.  Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems , 1982, TOMS.

[16]  Elizabeth A. Croft,et al.  Feed optimization for five-axis CNC machine tools with drive constraints , 2008 .

[17]  S. R. Wilson,et al.  Surface Figuring Using Neutral Ion Beams , 1989, Optics & Photonics.

[18]  Rida T. Farouki,et al.  Time-optimal traversal of curved paths by Cartesian CNC machines under both constant and speed-dependent axis acceleration bounds , 2007 .

[19]  A. Beaucamp,et al.  Comparison of tool feed influence in CNC polishing between a novel circular-random path and other pseudo-random paths. , 2017, Optics express.

[20]  C. Tsai,et al.  The Golden Section Search Algorithm for Finding a Good Shape Parameter for Meshless Collocation Methods , 2010 .

[21]  David D Walker,et al.  Pseudo-random tool paths for CNC sub-aperture polishing and other applications. , 2008, Optics express.

[22]  Tai Sheng Wang,et al.  Dwell time algorithm in ion beam figuring. , 2009, Applied optics.

[23]  M. Tsai,et al.  Development of a dynamics-based NURBS interpolator with real-time look-ahead algorithm , 2007 .

[24]  Steven Y. Liang,et al.  Inverse identification of Johnson-Cook material constants based on modified chip formation model and iterative gradient search using temperature and force measurements , 2019, The International Journal of Advanced Manufacturing Technology.

[25]  Li Sheng-yi.  Model and Method to Determine Dwell Time in Ion Beam Figuring , 2007 .

[26]  Yuwen Sun,et al.  A novel adaptive-feedrate interpolation method for NURBS tool path with drive constraints , 2014 .

[27]  Steven Y. Liang,et al.  Inverse determination of Johnson–Cook model constants of ultra-fine-grained titanium based on chip formation model and iterative gradient search , 2018, The International Journal of Advanced Manufacturing Technology.