射流抛光中生成高斯型去除函数的数学建模方法
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摘要
提出了一种高斯型去除(GTR)函数生成过程的数学建模方法。基于环路积分的思路,建立了一种旋转扫掠生成GTR函数的数学模型,明确了喷嘴高度为决定GTR函数形貌的关键工艺参数,验证了模型的正确性。在该模型的指导下,进一步研究了生成GTR函数的喷嘴高度范围和GTR函数的形貌变化规律,发现当回转中心与定点斜入射去除函数最深点重合时,生成的去除函数最接近理想高斯型。这对实际加工中工艺参数的优化具有理论指导意义。
A numerical modeling method for the generation of a Gaussian-type removal(GTR)function is proposed.Based on the idea of the loop integration,a mathematical model for the generation of GTR function by rotating sweep is established.It is clarified that the nozzle height is the key process parameter to determine the GTR function profile and the validity of this model is also verified.Under the guidance of this model,the nozzle height range for the generation of GTR function and the change law of GTR function profiles are further investigated,and it is found that the removal function obtained when the gyration center coincides with the deepest point of a removal function with a fixed oblique incidence is the closest to an ideal GTR function,which provides a theoretical guidance in the optimization of process parameters for the practical fabrication.
A numerical modeling method for the generation of a Gaussian-type removal(GTR)function is proposed.Based on the idea of the loop integration,a mathematical model for the generation of GTR function by rotating sweep is established.It is clarified that the nozzle height is the key process parameter to determine the GTR function profile and the validity of this model is also verified.Under the guidance of this model,the nozzle height range for the generation of GTR function and the change law of GTR function profiles are further investigated,and it is found that the removal function obtained when the gyration center coincides with the deepest point of a removal function with a fixed oblique incidence is the closest to an ideal GTR function,which provides a theoretical guidance in the optimization of process parameters for the practical fabrication.
引文
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[16]Wang J,Fan B,Wan Y J,et al.A method to evaluate the error restraint ability of CCOS process[J].Acta Photonica Sinica,2014,43(7):0722002.王佳,范斌,万勇建,等.一种评价CCOS抛光工艺误差抑制能力的方法[J].光子学报,2014,43(7):0722002.
[17]Chen X,Guo P J,Ren J F.Optimization of removal function in computer controlled optical surfacing[J].Proceedings of SPIE,2010,7655:76551Y.
[2]Yuan J L,Wu Z,LüB H,et al.Review on ultraprecision polishing technology of aspheric surface[J].Journal of Mechanical Engineering,2012,48(23):167.
[3]Fang H.Fluid jet polishing[D].Suzhou:Soochow University,2004.方慧.液体喷射抛光技术[D].苏州:苏州大学,2004.
[4]LüL,Ma P,Zhu H,et al.Effect of material removal function on surface shape error correction in fluid jet polishing[J].Chinese Journal of Lasers,2016,43(4):0416003.吕亮,马平,朱衡,等.水射流抛光去除函数对面形误差修正的影响[J].中国激光,2016,43(4):0416003.
[5]Jones R A.Computer simulation of smoothing during computer-controlled optical polishing[J].Applied Optics,1995,34(7):1162-1169.
[6]Booij S,Partosoebroto I,Braat J J M,et al.Computational model for prediction of shaping with FJP and experimental validation[J].Optical Fabrication and Testing,2002:OTuB1.
[7]Horiuchi O,Ikeno J,Shibutani H,etal.Nano-abrasion machining of brittle materials and its application to corrective figuring[J].Precision Engineering,2007,31(1):47-54.
[8]Fang H.Optimization of the material removal influid jet polishing[J].Optical Engineering,2006,45(5):053401.
[9]Yu Z R,Kuo C H,Hsu W Y,et al.Study of airdriving fluid jet polishing[J].Proceedings of SPIE,2011,8126:812611.
[10]Shi C Y,Yuan J H,Wu F,et al.Ultra-precision figuring using submerged jet polishing[J].Chinese Optics Letters,2011,9(9):092201.
[11]Booij S M.Fluid jet polishing-possibilities and limitations of a new fabrication technique[D].Delft:Delft University,2003.
[12]Li Z Z.Study on abrasive jet polishing technology[D].Changsha:National University of Defense Technology,2011:43-46.李兆泽.磨料水射流抛光技术研究[D].长沙:国防科技大学,2011:43-46.
[13]Li J,Zhang L X,Sun P F,et al.Fast-form experimental method of Gaussian shaped removal function of fluid jet polishing[J].Acta Optica Sinica,2018,38(7):0722002.李建,张连新,孙鹏飞,等.射流抛光高斯型去除函数的快速生成实验方法[J].光学学报,2018,38(7):0722002.
[14]Shi C Y,Yuan J H,Wu F,et al.Research of errors analysis and material removal stability in fluid jet polishing[J].Acta Optica Sinica,2011,31(1):0112012.施春燕,袁家虎,伍凡,等.射流抛光误差分析与材料去除稳定性研究[J].光学学报,2011,31(1):0112012.
[15]Shi C Y,Yuan J H,Wu F,et al.Influence of standoff distance on material removal function in fluid jet polishing[J].Infrared and Laser Engineering,2011,40(4):685-689.施春燕,袁家虎,伍凡,等.喷射距离对射流抛光去除函数的影响[J].红外与激光工程,2011,40(4):685-689.
[16]Wang J,Fan B,Wan Y J,et al.A method to evaluate the error restraint ability of CCOS process[J].Acta Photonica Sinica,2014,43(7):0722002.王佳,范斌,万勇建,等.一种评价CCOS抛光工艺误差抑制能力的方法[J].光子学报,2014,43(7):0722002.
[17]Chen X,Guo P J,Ren J F.Optimization of removal function in computer controlled optical surfacing[J].Proceedings of SPIE,2010,7655:76551Y.
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