Article(id=1315743677654348220, tenantId=1146029695717560320, journalId=1315121910733963395, issueId=1315743622176288781, articleNumber=null, orderNo=null, doi=10.3788/gzxb20265502.0222004, pmid=null, cstr=32255.14.gzxb20265502.0222004, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1756656000000, receivedDateStr=2025-09-01, revisedDate=null, revisedDateStr=null, acceptedDate=1758988800000, acceptedDateStr=2025-09-28, onlineDate=1791627338087, onlineDateStr=2026-10-10, pubDate=1771948800000, pubDateStr=2026-02-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1791627338087, onlineIssueDateStr=2026-10-10, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1791627338087, creator=13701087609, updateTime=1791627338087, updator=13701087609, issue=Issue{id=1315743622176288781, tenantId=1146029695717560320, journalId=1315121910733963395, year='2026', volume='55', issue='2', pageStart='1', pageEnd='326', issueExtLink='null', onlineDate='null', pubDate='1771948800000', pubDateStr='2026-02-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1791627324861, creator='13701087609', updateTime=1791627390701, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1315743898396381488, tenantId=1146029695717560320, journalId=1315121910733963395, issueId=1315743622176288781, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1315743898396381489, tenantId=1146029695717560320, journalId=1315121910733963395, issueId=1315743622176288781, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=97, endPage=112, ext={EN=ArticleExt(id=1315743677859869117, articleId=1315743677654348220, tenantId=1146029695717560320, journalId=1315121910733963395, language=EN, title=Simulation and Experimental Study on Thermal Field Control Rules for Surface Morphology of Metal Tin Polishing Pads, columnId=1315743623623332133, journalTitle=Acta Photonica Sinica, columnName=Optical Design and Fabrication, runingTitle=null, highlight=null, articleAbstract=

Large-aperture planar optical components are key parts of the optical systems in high-end equipment such as photolithography machines and laser fusion experimental devices. Full-aperture polishing, also known as continuous polishing, is an important processing method for large-aperture planar optical components. The surface conditioning of polishing pads has been a research focus for scholars both domestically and internationally. Existing research results indicate that effective conditioning is one of the primary factor to enhance the processing accuracy of optical components. For polishing pads with a meter-scale diameter, such as 1 200 mm, turning or grinding processes are typically employed to achieve surface conditioning. However, these methods are not only time-consuming but also struggle to achieve high-precision finishing on the pad surface. Efficient and high-precision conditioning of meter-scale polishing pad surfaces has long been a challenge in the optical component polishing process.

This paper proposes a method for surface topography conditioning of tin polishing pads through temperature field control. A composite polishing pad consisting of tin-aluminum-cast iron is constructed with three kinds of thin plates. A thermal field control system for the composite polishing pad is designed to investigate the internal temperature field distribution patterns of the pad under the influence of a controlled thermal field, and a gradient model of the internal temperature field within the composite polishing pad is established. Based on the bimetallic thermal deformation effect, five thermal stress distribution equations are established on the neutral surface of the three-layer composite polishing pad. By setting boundary conditions, a differential equation for thermal stress elastic deformation of the composite pad is established, and a mathematical model for surface thermal deformation of the tin polishing pad with parameter tcont as the variable is obtained through solving the equation.

Using finite element simulation software, a simulation analysis was conducted on the thermal deformation of the composite material polishing pad's surface. The ambient temperature field was set to 20 ℃, with constraints and a controlled thermal field applied to the bottom surface of the composite polishing pad. When the parameter tcont of the controlled thermal field was set between 16 and 19 ℃, the thermal deformation of the polishing pad's surface was simulated, and the contour, peak value, and average value of the thermal deformation were analyzed. The simulation results indicated that when the controlled thermal field parameter tcont was set to 20 ℃, there was no temperature gradient change within the composite polishing pad, and no thermal deformation occurred on its surface. However, when tcont was less than 20 ℃, the composite material polishing pad exhibited an overall concave-shaped thermal deformation, and the magnitude of the thermal deformation became more pronounced as tcont decreased. Experiments were conducted to validate the regulation law of the thermal field on the surface of a tin polishing pad. Ensuring an ambient temperature of 20 ℃ in a constant-temperature workshop, measurement tools such as laser displacement sensors were used to measure the surface of the polishing pad. The deformation law of the polishing pad's surface was examined at parameter tcont values ranging from 16 to 19 ℃. Finally, through nine sets of processing experiments on optical components, the impact of the parameter tcont on the processing results was verified. The experimental and simulation results showed consistency in the trend of thermal deformation of the polishing pad's surface. Moreover, by adjusting the thermal field control parameter tcont, the surface accuracy of the processed optical components was optimized.

Through theoretical analysis, simulation, and experimental verification, the paper draws the following conclusions: 1) A controllable thermal deformation prediction mathematical model for the surface topography of the polishing pad was established based on the multi-metallic thermal deformation effect; 2) A finite element model for thermal field regulation of the polishing pad was developed and experimentally validated. Within the temperature range tcont of 16 ℃ to 19 ℃, the finite element analysis results of thermal deformation of the polishing pad were consistent with the experimental results in terms of their changing trends; 3) The thermal deformation generated by the polishing pad thermal field regulation system is the greatest at tcont=16 ℃, with a maximum deformation of 16.9 μm and an average deformation of 12.5 μm; it is the smallest at t=19 ℃, with a maximum deformation of 2.2 μm and an average deformation of 2 μm; 4) Adjusting the parameter tcont can enhance the processing accuracy of the component surface. When tcont=18 ℃, the polishing accuracy of planar optical components is the highest. Compared to when tcont=20 ℃ and tcont=16 ℃, the surface accuracy PV value improves by an average of 20%, and the RMS value improves by an average of 15%; 5) According to the comparative analysis, the mathematical model of thermal deformation on the polishing pad surface and the simulation analysis cannot accurately predict specific values of the thermal deformation. Precise model analysis will be conducted in subsequent research.

, authors=Lingyu ZHAO1, Zecun GAO1, Huiying ZHAO2, authorsList=Lingyu ZHAO, Zecun GAO, Huiying ZHAO, authorCompany=null, correspAuthors=Lingyu ZHAO, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1315743682058367450, articleId=1315743677654348220, tenantId=1146029695717560320, journalId=1315121910733963395, language=CN, title=金属锡抛光垫表面形貌热场调控规律仿真及实验研究, columnId=1315743623807881511, journalTitle=光子学报, columnName=光学设计与制造, runingTitle=null, highlight=null, articleAbstract=

平面抛光是400 mm × 400 mm口径平面光学元件的重要加工工艺,抛光垫修整是提高连续抛光加工效果的重要手段。抛光垫表面轮廓的高效、高精度的修整一直是行业的一个重要的研究方向和难点。提出一种金属锡抛光垫表面形貌的热场调控方法,在双金属热变形效应的基础上,对三种材料组成的复合抛光盘内部温度场以及热应力进行了分析,构建了金属锡抛光垫的表面形貌热场调控数学模型。利用ANSYS仿真以及实验对金属锡抛光垫表面形貌热场调控进行了验证。研究结果表明,通过调节热场温度参数tcont使得抛光垫表面形貌产生热变形,当tcont等于16 ℃时,抛光垫表面形貌的热变形最大,为16.9 μm;当tcont等于19 ℃时,抛光垫表面的热变形最小,为2.2 μm。最后,进行9组元件抛光工艺实验,当tcont等于18 ℃时,平面光学元件抛光精度最高,面形精度峰谷值平均提升20%,均方根值平均提升15%。

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Nuclear Materials and Energy, 2018, 16:128-132., articleTitle=Surface morphology of Tungsten-F82H after high-heat flux testing using plasma-arc lamps, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1315743682301637083, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, xref=1, ext=[AuthorCompanyExt(id=1315743682330997212, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, companyId=1315743682301637083, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1Beijing Institute of Petrochemical Technology, School of Mechanical Engineering, Beijing 102627, China), AuthorCompanyExt(id=1315743682343580125, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, companyId=1315743682301637083, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1北京石油化工学院 机械工程学院, 北京 102627)]), AuthorCompany(id=1315743682431660510, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, xref=2, ext=[AuthorCompanyExt(id=1315743682448437727, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, companyId=1315743682431660510, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2Xi'an Jiaotong University, School of Mechanical Engineering, Xi'an 710049, China), AuthorCompanyExt(id=1315743682456826336, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, companyId=1315743682431660510, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2西安交通大学 机械工程学院, 西安 710049)])], figs=[ArticleFig(id=1315743685606748666, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=EN, label=Fig.1, caption=Structural schematic diagram of polishing pad thermal field regulation system, figureFileSmall=NKgJVrwt8ZICBoi7Qj/ZQw==, figureFileBig=l6/EPwOdUE0yjw5U0ywTxg==, tableContent=null), ArticleFig(id=1315743685690634747, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=CN, label=图1, caption=抛光垫热场调控系统的结构简图, figureFileSmall=NKgJVrwt8ZICBoi7Qj/ZQw==, figureFileBig=l6/EPwOdUE0yjw5U0ywTxg==, tableContent=null), ArticleFig(id=1315743685891961340, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=EN, label=Fig.2, caption=Principle model of thermal field regulation for of metal tin polishing pad surface, figureFileSmall=nE0JLrrUp7+zvW4D2hWYqA==, figureFileBig=52itNWCSfCkuFjS3ako0Dw==, tableContent=null), ArticleFig(id=1315743685959070205, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=CN, label=图2, caption=金属锡抛光垫表面轮廓热场调控原理模型, figureFileSmall=nE0JLrrUp7+zvW4D2hWYqA==, figureFileBig=52itNWCSfCkuFjS3ako0Dw==, tableContent=null), ArticleFig(id=1315743686026179070, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=EN, label=Fig.3, caption=Two types of thermal stress models for composite pads, figureFileSmall=w4LErWrP+Re3cEQCmWxDVQ==, figureFileBig=q6aPHwbdo30YBfzWA0nrFA==, tableContent=null), ArticleFig(id=1315743686110065151, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=CN, label=图3, caption=复合盘两类热应力模型, figureFileSmall=w4LErWrP+Re3cEQCmWxDVQ==, figureFileBig=q6aPHwbdo30YBfzWA0nrFA==, tableContent=null), ArticleFig(id=1315743686181368320, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=EN, label=Fig.4, caption=Simplified mechanical model of thermal deformation for composite pads. 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Material properties of parts

, figureFileSmall=null, figureFileBig=null, tableContent=
NameMaterialCoefficient of thermal expansion/K-1
Aluminum diskAluminium alloy23.0 × 10-6[21]
Cast iron diskHT30010.0 × 10-6[22]
Cooling water chamberHT30010.0 × 10-6[22]
), ArticleFig(id=1315743689465508375, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=CN, label=表1, caption=

主要零件所用材料

, figureFileSmall=null, figureFileBig=null, tableContent=
NameMaterialCoefficient of thermal expansion/K-1
Aluminum diskAluminium alloy23.0 × 10-6[21]
Cast iron diskHT30010.0 × 10-6[22]
Cooling water chamberHT30010.0 × 10-6[22]
), ArticleFig(id=1315743689528422936, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=EN, label=Table 2, caption=

Relationship between temperature parameters and thermal deformation of composite disks

, figureFileSmall=null, figureFileBig=null, tableContent=
tcontMinimum deformationMaximum deformationAverage deformation
16 ℃024.8 μm7.4 μm
17 ℃010.7 μm3.9 μm
18 ℃07.2 μm2.6 μm
19 ℃03.6 μm1.3 μm
), ArticleFig(id=1315743689603920409, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=CN, label=表2, caption=

热场温度参数与复合盘热变形关系

, figureFileSmall=null, figureFileBig=null, tableContent=
tcontMinimum deformationMaximum deformationAverage deformation
16 ℃024.8 μm7.4 μm
17 ℃010.7 μm3.9 μm
18 ℃07.2 μm2.6 μm
19 ℃03.6 μm1.3 μm
), ArticleFig(id=1315743689692000794, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=EN, label=Table 3, caption=

Parameter setting of polishing pad measurement

, figureFileSmall=null, figureFileBig=null, tableContent=
TypeRepetition accuracy/μmMovement speed/(mm·min-1)Number of measurementsSampling frequency/Hz
LK-H020,KEYENCE0.023001250
), ArticleFig(id=1315743689784275483, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=CN, label=表3, caption=

抛光垫测量的基本参数设定

, figureFileSmall=null, figureFileBig=null, tableContent=
TypeRepetition accuracy/μmMovement speed/(mm·min-1)Number of measurementsSampling frequency/Hz
LK-H020,KEYENCE0.023001250
), ArticleFig(id=1315743689863967260, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=EN, label=Table 4, caption=

Experimental parameters for thermal deformation of polishing pads

, figureFileSmall=null, figureFileBig=null, tableContent=
tcont/℃ tinter/℃Thermal deformation of polishing pad surface/μm
1620 ΔZi(tcont)=Zi(tcont)-Zi, FPV, FRMS
17
18
19
), ArticleFig(id=1315743689943659037, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=CN, label=表4, caption=

热光垫热变形实验参数

, figureFileSmall=null, figureFileBig=null, tableContent=
tcont/℃ tinter/℃Thermal deformation of polishing pad surface/μm
1620 ΔZi(tcont)=Zi(tcont)-Zi, FPV, FRMS
17
18
19
), ArticleFig(id=1315743690019156510, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=EN, label=Table 5, caption=

Processing parameters of planar optical elements

, figureFileSmall=null, figureFileBig=null, tableContent=
Component materialDiameter/mmPolishing padRotating speed of turntable/(r·min-1)Rotating speed of workpiece/(r·min-1)Slurry
Fused quartz120Metal tin plate109.9Al2O3
), ArticleFig(id=1315743690103042591, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=CN, label=表5, caption=

平面光学元件加工参数

, figureFileSmall=null, figureFileBig=null, tableContent=
Component materialDiameter/mmPolishing padRotating speed of turntable/(r·min-1)Rotating speed of workpiece/(r·min-1)Slurry
Fused quartz120Metal tin plate109.9Al2O3
), ArticleFig(id=1315743690178540064, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=EN, label=Table 6, caption=

Nine experimental schemes for planar optical elements

, figureFileSmall=null, figureFileBig=null, tableContent=
Number tcont/℃Surface accuracy(PV)/λSurface accuracy(RMS)/λ
1161.030.20
2160.830.18
3160.900.20
4180.750.16
5180.680.15
6180.800.18
7200.830.19
8200.840.19
9200.780.16
), ArticleFig(id=1315743690266620449, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=CN, label=表6, caption=

平面光学元件9组加工实验的方案

, figureFileSmall=null, figureFileBig=null, tableContent=
Number tcont/℃Surface accuracy(PV)/λSurface accuracy(RMS)/λ
1161.030.20
2160.830.18
3160.900.20
4180.750.16
5180.680.15
6180.800.18
7200.830.19
8200.840.19
9200.780.16
), ArticleFig(id=1315743690333729314, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=EN, label=Table 7, caption=

Maximum and average values of thermal deformation on the surface of the thermal pad

, figureFileSmall=null, figureFileBig=null, tableContent=
tcontMinimum deformationMaximum deformationAverage deformation
16 ℃016.9 μm12.5 μm
17 ℃011.1 μm8.8 μm
18 ℃06.2 μm5.0 μm
19 ℃02.2 μm2.0 μm
), ArticleFig(id=1315743690400838179, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=CN, label=表7, caption=

热光垫表面热变形的最大值和平均值

, figureFileSmall=null, figureFileBig=null, tableContent=
tcontMinimum deformationMaximum deformationAverage deformation
16 ℃016.9 μm12.5 μm
17 ℃011.1 μm8.8 μm
18 ℃06.2 μm5.0 μm
19 ℃02.2 μm2.0 μm
), ArticleFig(id=1315743690467947044, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=EN, label=Table 8, caption=

Nine experimental results of planar optical elements

, figureFileSmall=null, figureFileBig=null, tableContent=
NumberTemperature of water cooler/℃Surface accuracy(PV)/λSurface accuracy(RMS)/λAverage value(PV)/λAverage value(RMS)/λ
1161.030.200.920.19
2160.830.18
3160.900.20
4180.750.160.740.16
5180.680.15
6180.800.18
7200.830.190.810.18
8200.840.19
9200.780.16
), ArticleFig(id=1315743690543444517, tenantId=1146029695717560320, journalId=1315121910733963395, articleId=1315743677654348220, language=CN, label=表8, caption=

平面光学元件9组加工实验的结果

, figureFileSmall=null, figureFileBig=null, tableContent=
NumberTemperature of water cooler/℃Surface accuracy(PV)/λSurface accuracy(RMS)/λAverage value(PV)/λAverage value(RMS)/λ
1161.030.200.920.19
2160.830.18
3160.900.20
4180.750.160.740.16
5180.680.15
6180.800.18
7200.830.190.810.18
8200.840.19
9200.780.16
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金属锡抛光垫表面形貌热场调控规律仿真及实验研究
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赵凌宇 1 , 高泽村 1 , 赵惠英 2
光子学报 | 光学设计与制造 2026,55(2): 97-112
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光子学报 |光学设计与制造 2026 , 55 (2) : 97 -112
金属锡抛光垫表面形貌热场调控规律仿真及实验研究
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赵凌宇1 , 高泽村1, 赵惠英2
作者信息
  • 1北京石油化工学院 机械工程学院, 北京 102627
  • 2西安交通大学 机械工程学院, 西安 710049
通讯作者:
赵凌宇,
作者简介:

赵凌宇,

Simulation and Experimental Study on Thermal Field Control Rules for Surface Morphology of Metal Tin Polishing Pads
Lingyu ZHAO1 , Zecun GAO1, Huiying ZHAO2
Affiliations
  • 1Beijing Institute of Petrochemical Technology, School of Mechanical Engineering, Beijing 102627, China
  • 2Xi'an Jiaotong University, School of Mechanical Engineering, Xi'an 710049, China
出版时间: 2026-02-25 doi: 10.3788/gzxb20265502.0222004
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平面抛光是400 mm × 400 mm口径平面光学元件的重要加工工艺,抛光垫修整是提高连续抛光加工效果的重要手段。抛光垫表面轮廓的高效、高精度的修整一直是行业的一个重要的研究方向和难点。提出一种金属锡抛光垫表面形貌的热场调控方法,在双金属热变形效应的基础上,对三种材料组成的复合抛光盘内部温度场以及热应力进行了分析,构建了金属锡抛光垫的表面形貌热场调控数学模型。利用ANSYS仿真以及实验对金属锡抛光垫表面形貌热场调控进行了验证。研究结果表明,通过调节热场温度参数tcont使得抛光垫表面形貌产生热变形,当tcont等于16 ℃时,抛光垫表面形貌的热变形最大,为16.9 μm;当tcont等于19 ℃时,抛光垫表面的热变形最小,为2.2 μm。最后,进行9组元件抛光工艺实验,当tcont等于18 ℃时,平面光学元件抛光精度最高,面形精度峰谷值平均提升20%,均方根值平均提升15%。

热场调控  /  抛光垫修整  /  平面连续抛光  /  光学元件  /  超精密加工

Large-aperture planar optical components are key parts of the optical systems in high-end equipment such as photolithography machines and laser fusion experimental devices. Full-aperture polishing, also known as continuous polishing, is an important processing method for large-aperture planar optical components. The surface conditioning of polishing pads has been a research focus for scholars both domestically and internationally. Existing research results indicate that effective conditioning is one of the primary factor to enhance the processing accuracy of optical components. For polishing pads with a meter-scale diameter, such as 1 200 mm, turning or grinding processes are typically employed to achieve surface conditioning. However, these methods are not only time-consuming but also struggle to achieve high-precision finishing on the pad surface. Efficient and high-precision conditioning of meter-scale polishing pad surfaces has long been a challenge in the optical component polishing process.

This paper proposes a method for surface topography conditioning of tin polishing pads through temperature field control. A composite polishing pad consisting of tin-aluminum-cast iron is constructed with three kinds of thin plates. A thermal field control system for the composite polishing pad is designed to investigate the internal temperature field distribution patterns of the pad under the influence of a controlled thermal field, and a gradient model of the internal temperature field within the composite polishing pad is established. Based on the bimetallic thermal deformation effect, five thermal stress distribution equations are established on the neutral surface of the three-layer composite polishing pad. By setting boundary conditions, a differential equation for thermal stress elastic deformation of the composite pad is established, and a mathematical model for surface thermal deformation of the tin polishing pad with parameter tcont as the variable is obtained through solving the equation.

Using finite element simulation software, a simulation analysis was conducted on the thermal deformation of the composite material polishing pad's surface. The ambient temperature field was set to 20 ℃, with constraints and a controlled thermal field applied to the bottom surface of the composite polishing pad. When the parameter tcont of the controlled thermal field was set between 16 and 19 ℃, the thermal deformation of the polishing pad's surface was simulated, and the contour, peak value, and average value of the thermal deformation were analyzed. The simulation results indicated that when the controlled thermal field parameter tcont was set to 20 ℃, there was no temperature gradient change within the composite polishing pad, and no thermal deformation occurred on its surface. However, when tcont was less than 20 ℃, the composite material polishing pad exhibited an overall concave-shaped thermal deformation, and the magnitude of the thermal deformation became more pronounced as tcont decreased. Experiments were conducted to validate the regulation law of the thermal field on the surface of a tin polishing pad. Ensuring an ambient temperature of 20 ℃ in a constant-temperature workshop, measurement tools such as laser displacement sensors were used to measure the surface of the polishing pad. The deformation law of the polishing pad's surface was examined at parameter tcont values ranging from 16 to 19 ℃. Finally, through nine sets of processing experiments on optical components, the impact of the parameter tcont on the processing results was verified. The experimental and simulation results showed consistency in the trend of thermal deformation of the polishing pad's surface. Moreover, by adjusting the thermal field control parameter tcont, the surface accuracy of the processed optical components was optimized.

Through theoretical analysis, simulation, and experimental verification, the paper draws the following conclusions: 1) A controllable thermal deformation prediction mathematical model for the surface topography of the polishing pad was established based on the multi-metallic thermal deformation effect; 2) A finite element model for thermal field regulation of the polishing pad was developed and experimentally validated. Within the temperature range tcont of 16 ℃ to 19 ℃, the finite element analysis results of thermal deformation of the polishing pad were consistent with the experimental results in terms of their changing trends; 3) The thermal deformation generated by the polishing pad thermal field regulation system is the greatest at tcont=16 ℃, with a maximum deformation of 16.9 μm and an average deformation of 12.5 μm; it is the smallest at t=19 ℃, with a maximum deformation of 2.2 μm and an average deformation of 2 μm; 4) Adjusting the parameter tcont can enhance the processing accuracy of the component surface. When tcont=18 ℃, the polishing accuracy of planar optical components is the highest. Compared to when tcont=20 ℃ and tcont=16 ℃, the surface accuracy PV value improves by an average of 20%, and the RMS value improves by an average of 15%; 5) According to the comparative analysis, the mathematical model of thermal deformation on the polishing pad surface and the simulation analysis cannot accurately predict specific values of the thermal deformation. Precise model analysis will be conducted in subsequent research.

Thermal field control  /  Dressing of polishing pad  /  Continuous polishing of flat surfaces  /  Optical components  /  Ultra-precision machining
赵凌宇, 高泽村, 赵惠英. 金属锡抛光垫表面形貌热场调控规律仿真及实验研究. 光子学报, 2026 , 55 (2) : 97 -112 . DOI: 10.3788/gzxb20265502.0222004
Lingyu ZHAO, Zecun GAO, Huiying ZHAO. Simulation and Experimental Study on Thermal Field Control Rules for Surface Morphology of Metal Tin Polishing Pads[J]. Acta Photonica Sinica, 2026 , 55 (2) : 97 -112 . DOI: 10.3788/gzxb20265502.0222004
大口径平面光学元件是高端装备(例如光刻机、激光聚变实验装置等)光学系统的重要零件,随着装备性能的不断提升,对其加工精度的要求也逐步提高。以美国国家点火装置为例,其光学系统包含了7 000片以上的大口径光学元件(平面元件数量超过70%),口径≥400 mm×400 mm,面形低频轮廓误差要求优于1/3 λ(λ = 632.8 nm)[1-2]。同样,半导体加工光刻过程所需的光掩模基板也提出了亚微米甚至纳米级面形轮廓精度的加工需求。由于极端的尺寸、精度及材料特性,大口径平面光学元件的高效、高精度制造一直是行业的难点。
全口径抛光,即连续抛光是大口径平面光学元件的重要加工手段,通常位于磨削工艺和子口径抛光工艺中间,它可以去除磨削阶段产生的亚表面损伤,同时具备更好的中频加工性能,在全工艺链条中兼顾精度和效率,是平面光学元件高质量加工的重要保障。国内外学者针对连续抛光技术开展了大量的研究工作[3-7],抛光垫的表面修整是一个主要的研究方向。WANG Z P等[8]针对抛光垫修整模拟平台,提出了一种基于配点网格法和参数映射的低成本数值方法,从而显著减少工艺开发周期的时间和成本。SEO J等[9]提出一种利用具备形状记忆且加热后能恢复形状功能的聚氨酯基原材料修整抛光垫表面的方法,实验验证该方法可提高化学机械抛光(Chemical Mechanical Polishing, CMP)的性能并延长抛光垫的使用寿命。ZHENG Y等[10]利用磨料水射流技术对固结磨料抛光垫进行修整,研究不同压力下磨料水射流对固结磨料抛光垫进行修整影响效果。WANG Z K等[11]针对现有固结磨料修整技术中修整效果差、研磨垫损伤程度高等问题,提出了一种利用磨料水射流进行修整的新技术,采用自主研发的磨料水射流系统,对含铜量为30%的固结磨料研磨垫进行了修整试验。LI X等[12]研究高压微射流(High Pressure Micro Jet, HPMJ)修整技术对聚氨酯、阻尼布和无纺布修整的效果。SON J等[13]提出一种接触面积可变的抛光垫修整系统,并利用该系统对提高抛光垫寿命进行了初步研究,抛光垫寿命可延长至20 h以上。上述研究结果都表明,抛光垫表面形貌修整是提高光学元件加工精度的主要手段之一,可以改善抛光加工的光学元件面形精度、提高材料去除率(Material Removal Rate, MRR),降低表面粗糙度等[14-17]。
然而,在持续不断的抛光加工过程中,抛光垫的表面会在抛光颗粒的作用下产生磨损,进而诱发釉化、钝化等问题,并且会导致抛光加工工艺性能降低[18]。因此需要对抛光垫表面微观形貌进行往复修整以改善元件的加工效果。由此可见,抛光垫表面的修整工艺是平面元件抛光加工中的关键步骤,对于优化加工效果起到重要影响[19-20]。米级口径抛光垫常采用金属切削或金刚石磨削的方式对其表面进行修整,这种方法需要消耗大量的时间,也极难保证抛光垫表面的高精度修整,平面抛光的米级口径抛光垫表面高效、高精度修整一直是光学元件加工的难点。
本文提出一种金属抛光垫动态热场的修整方法,和传统机械修整或水射流修整方法相比,动态热场修整法不会引起抛光垫的额外损耗,间接提高寿命,此外,它是一种实时的修整方法,修整时可持续对元件进行抛光加工,具备高效、确定性控制、材料无损耗等特性。本文建立了抛光垫动态热场系统的物理模型,推导抛光垫热场修整的热变形数学方程,利用ANSYS软件对抛光垫热变形进行了模拟,最后通过实验,对动态热场抛光修整以及平面元件的加工效果进行验证。
金属锡盘抛光垫热场调控系统主要由复合抛光盘(即复合盘,由抛光垫、铝盘、铸铁盘组成)、热源调控系统2个部分组成,它的整体结构沿C轴回转对称,如图1所示。
铝盘以及铸铁盘为实心金属圆盘,它们基本尺寸分别为πd1×h1(d1 = 1 200 mm, h1 = 45 mm)和πd2×h2(d2 = 1 200 mm, h2 = 20 mm)。热源调控系统由水槽、循环冷却水以及水冷机等部分组成。金属锡盘抛光垫表面形貌热场调控系统的铝盘、铸铁盘、水槽之间采用刚性连接方式,各零件所用材料以及热膨胀系数见表1。根据弹性力学中圆形薄板变形理论,不同材料薄板进行刚性连接后,当薄板温度场发生变化时,各金属不同的膨胀系数,将导致薄板内部产生热应力,进而引起薄板的挠曲变形,简称双金属热变形效应。
金属锡盘抛光垫表面形貌热场调控系统的复合盘温度场由冷却水进行控制。冷却水的温度发生改变时,在双金属效应作用下,复合盘将产生挠曲变形,这种变形最终会作用到抛光垫上,从而引起抛光垫表面各点沿数值方向产生不同程度位移,进而实现对抛光垫表面形状的修整。
金属锡抛光垫表面轮廓热场调控原理模型如图2所示,复合盘(抛光垫、铝盘、铸铁盘)直径为1 200 mm,总厚度≤ 100 mm,径/厚比为12∶1,忽略侧面热场作用,复合盘即抛光垫表面轮廓热变形主要由2种温度场,即抛光垫上表面温度场和动态热场共同作用决定。抛光垫上表面温度场主要受抛光界面影响,为简化计算,设抛光垫上表面温度场沿抛光垫表面均匀分布,温度参数为tinter;动态热场沿铸铁盘底部均匀分布,温度参数为tcont。
根据热传导原理,2种温度场热量在抛光垫—铝盘—铸铁盘间传导。假设温度传导为理想状态,复合盘任意高度截面的温度均匀分布,温度场沿厚度h方向呈线性梯度变化,则复合盘温度场可以表示为
T(h)=tinter-tconth0+h1+h2h+tcont
式中,T(h)表示复合盘温度场函数;h表示复合盘沿厚度方向的高度,定义铸铁盘底面高度为0。
双层复合材料的热应力由两部分组成,一部分是单一材料由温度梯度变化导致的温度梯度热应力σgrad,可以表示为[23]
σgrad=EαΔT2(1-ν)
式中,E表示材料的弹性模量;α表示材料的热膨胀系数;ΔT表示稳态下材料上表面与下表面的温度差;ν表示材料的泊松比。第二部分是两材料间由不同线胀系数导致的双金属热应力σbime,可以表示为[23]
σbime=Ea(α1-α2)ΔTrise
式中,Ea表示两种材料的平均弹性模量;α1表示材料1的热膨胀系数;α2表示材料2的热膨胀系数;ΔTrise表示两种材料的平均温度差。
因此,复合盘热应力主要由两类应力构成,如图3所示,分别是抛光垫D1、铝盘D2、铸铁盘D3由温度梯度引起的梯度热应力和抛光垫—铝盘以及铝盘—铸铁间由不同材料热胀系数引起的双金属热应力。
根据式(1)和(2),抛光垫由温度场引起的温度梯度热应力σgradD1可以表示为
σgradD1=ED1αD12(1-νD1)(tinter-tcont)h0h0+h1+h2
式中,ED1表示抛光垫材料的弹性模量;αD1表示抛光垫材料的热膨胀系数;νD1表示抛光垫材料的泊松比。同理,铝盘由温度场梯度引起的温度梯度热应力σgradD2可以表示为
σgradD2=ED2αD22(1-νD2)(tinter-tcont)h1h0+h1+h2
式中,ED2表示铝盘材料的弹性模量;αD2表示铝盘材料的热膨胀系数;νD2表示铝盘材料的泊松比。同理,铸铁盘由温度场梯度引起的温度梯度热应力σgradD3可以表示为
σgradD3=ED3αD32(1-νD3)(tinter-tcont)h2h0+h1+h2
式中,ED3表示铸铁盘材料的弹性模量;αD3表示铸铁盘材料的热膨胀系数;νD3表示铸铁盘材料的泊松比。抛光垫—铝盘组成的双金属盘引起的双金属应力σbimeD1D2可以表示为
σbimeD1D2=14(ED1+ED2)(αD1-αD2)(tinter-tcont)h0+h1h0+h1+h2
同理,铝盘—铁盘组成的双金属盘引起的双金属应力σbimeD2D3可以表示为
σbimeD2D3=14(ED2+ED3)(αD2-αD3)(tinter-tcont)h1+h2h0+h1+h2
根据弹性力学的变形理论,复合薄板中性面内的纵向力不会产生挠曲变形,而横向力会使得薄板产生挠曲变形。设热应力σgradD1、σgradD2、σgradD3、σbimeD1D2、σbimeD2D3在复合盘中性面内引起的等效横向力为qt,在qt的作用下,复合盘会产生挠曲变形,它的力学模型如图4所示。则w和Mρ的弹性变形微分方程可以分别表示为
Dd2dρ2+1ρddρd2wdρ2+1ρdwdρ=qt
Mρ=-D∂2w∂ρ2+μ1ρ∂w∂ρ+1ρ2∂2w∂φ2
式中,w表示复合盘在中性面应力qt下产生的弯曲变形(挠度);ρ表示径向距离;D表示复合盘的等效弯曲刚度;Mρ表示等效力矩;μ表示复合盘的等效泊松比;φ表示w在极坐标下w(ρ,φ)中的角度位置。
式(9)为常微分方程,它的通解形式可以表示为
w=C1lnρ+C2ρ2lnρ+C3ρ2+C4+qtρ464D
式中,C1、C2、C3、C4表示任意常数,通过边界条件求解。
为对常数进行求解,假设两个边界条件。边界条件1:假设复合盘没有中心孔;边界条件2:假设复合盘采用简支边约束方式,因此有复合盘在qt作用下的挠曲变形曲线方程w为
w=qta464D1-ρ2a25+μ1+μ-ρ2a2
式中,a表示复合盘的半径。由式(12)可知,在ρ=0的位置,薄板的挠曲变形w为最大值,即
wmax=qta464D5+μ1+μ
热应力σgradD1、σgradD2、σgradD3、σbimeD1D2、σbimeD2D3等效作用在复合盘中性面内。根据边界条件2,复合盘的中性面的水平面方向没有材料热膨胀,膨胀沿复合盘中性面的垂直方向产生,因此,5个热应力的作用方向为垂直于中性面,复合盘中性面的应力qt可以表示为(等效面上做积分)
qt=∬s(σgradD1+σgradD2+σgradD3+σbimeD1D2+σbimeD2D3)ds
式中,s表示复合盘中性面的全表面;ds表示复合盘中性面全表面微分。
将式(4)~(8)带入到式(14)中可得
qt=πa2(∑i=15βi)(tinter-tcont)β1=ED1αD12(1-νD1)h0h0+h1+h2β2=ED2αD22(1-νD2)h1h0+h1+h2β3=ED3αD32(1-νD3)h2h0+h1+h2β4=14(ED1+ED2)(αD1-αD2)h0+h1h0+h1+h2β5=14(ED2+ED3)(αD2-αD3)h1+h2h0+h1+h2
将式(15)带入到式(12)和(13),复合盘任意位置热变形和热变形的最大值可以表示为
w=πa664D1-ρ2a25+μ1+μ-ρ2a2∑i=15βi(tinter-tcont)wmax=πa664D5+μ1+μ∑i=15βi(tinter-tcont)
式(16)揭示了金属锡盘抛光垫表面形貌热场调控原理,通过对参数tcont的控制可以完成对抛光垫表面形貌调节。上述理论推导过程中对诸多因素进行了理想化处理,因此式(16)只用作原理解释,不用于描述金属锡盘抛光垫表面形貌热场调控的精确模型。
采用ANSYS对复合盘的热变形进行稳态热仿真分析,仿真分析模型如图5所示,环境温度设定为20 ℃,在复合盘底部外圈施加固定支撑,底面全表面施加均匀分布的温度场tcont,温度场的参数分别设定为16 ℃、17 ℃、18 ℃、19 ℃和20 ℃,为保证仿真的准确性,热仿真的作用时间设定为2 400 s。
复合盘热变形仿真结果如图6所示。首先,当调控热场参数tcont = 20 ℃时,复合盘内部无温度梯度变化,抛光盘表面无热变形产生。然而当tcont≠ 20 ℃时,复合盘整体呈现不同的情况,在tcont = 16 ℃时,复合盘整体产生较大形变,首先热变形沿复合盘旋转轴线C中心对称,复合盘外圈热变形量最小为wρ=600 = 0,随着径向距离ρ不断地减小(即沿径向直线向中心轴收缩),抛光盘表面各点变形w不断地增加,当ρ接近中心轴时(ρ= 10 mm),抛光盘表面热变形位移为最大值,此时wρ=10= 24.8 μm。此外,复合盘整体各点变形量w为负值,即抛光盘表面呈现下凹形状,且变形曲线w(ρ)为非线性曲线。
当tcont分别为17 ℃、18 ℃和19 ℃的时候,复合盘整体呈现出类似变形规律,热变形沿旋转轴线C中心对称,外圈变形量最小,并随径向距离ρ不断地减小(即沿径向直线向中心轴收缩),抛光盘表面各变形w不断地增加。tcont在不同温度参数下,复合盘热变形平均值和最大变形量仿真结果如表2所示,以下内容在3.3节进行进一步展开讨论。
采用自主研制的1 200 mm口径抛光机床进行实验,测量原理如图7所示,激光位移传感器(型号:LK-H020,基恩士,重复精度0.02 μm)布置在机床修整轴上,可沿X向进行运动,金属锡抛光垫由转台带动绕C轴转动,利用激光位移传感器对抛光垫表面热变形进行测量。
设抛光垫表面轮廓测量点均匀分布,用Aij表示,其中i=1,2,…,n;j=1,2,…,m;n表示抛光垫表面各径向线测量点数量,m表示径向线的数量。设点Aij的相对高度为Δzij,采用极坐标表示,有Δzij(ρi,θj),则测量点数据集合S表示抛光垫表面轮廓,即
S=Δzij(ρi,θj)i=1,2,…,n;j=1,2,…,m
式中,ρi表示点Aij到O1点的距离;θj表示直线O1Aij与X轴夹角。设
Δzij=zij-Eij
式中,zij表示点Aij的测量结果;Eij表示点Aij的测量误差。根据图7分析Eij主要由抛光垫旋转轴在XOZ面倾角引起的Z向测量误差以及X轴在运动过程中在XOZ面引起的Z向误差组成,Eij表示为
Eij=δij+ηij+E0;i=1,2,…,n;j=1,2,…,m
式中,δij表示X轴导轨副运动过程中在XOZ面引起的Z向测量误差;ηij表示转台C轴在XOZ面内倾角引起的Z向测量误差;E0表示其他误差,服从正态分布,计算中用“0”表示。
δij及ηij由X轴及C轴运动副基准面几何形状决定,属于系统误差,可通过测量进行标定。δij的标定方案如图8所示,利用“00级”平尺对δij进行测量。
激光位移传感器沿X轴直线运动,对平尺表面进行测量,假设平尺是“绝对”平面,因此有
δij=-z1(ρi),i=1,2,…,n;j=1,2,…,m
式中,z1(ρi)表示测量点距离坐标原点O1的距离为ρi时位移传感器的测量数值。
根据图9(a)ηij可以表示为
ηij=tan(αj)×ρi≈αj×ρi,i=1,2,…,n;j=1,2,…,m
式中,αj表示转台旋转角度为-θj时,轴线在ZOX面内的倾角误差。采用电子水平仪对αj进行测量,测量方案如图9(b)。抛光垫旋转到-θj位置时,将电子水平仪放置在位置1处,测量结果为bj(μm/m);抛光垫旋转到-θj+180°的位置,水平仪运动到位置2处,测量结果为cj,αj表示为
αj=(bj-cj)2,j=1,2,…,m
因此,将式(22)代入到式(21),则有
ηij=bj-cj2×ρi,i=1,2,…,n;j=1,2,…,m
将式(19)、(20)和(23)代入到式(18)中可得
Δzij(ρi,θj)=zij+z1(ρi)+cj-bj2×ρi,i=1,2,…,n;j=1,2,…,m
式(24)为误差分离后的抛光垫表面轮廓数学模型,集合S=Δzij(ρi,θj)i=1,2,…,n;j=1,2,…,m表示抛光垫的表面轮廓形状。
抛光垫表面轮廓形状测量实验布置方案如图10所示。
设激光位移传感器的采样频率为f(Hz),X轴的进给速度为v(mm/min),ρ0为第一个点的起始坐标,则
ρi=ρ0+(i-1)v60f,i=1,2,…,n
假设θ1=0且各径向测量线360°周向等分抛光垫的表面,则θj可以表示为
θj=(j-1)j2π,j=1,2,…,m
定义ΔZi(tcont)是金属锡盘抛光垫表面Ai点的热变形位移,它表示为
ΔZi(tcont)=Zi(tcont)-Zi
式中,ΔZi(tcont)表示热场调控参数tcont作用下抛光垫表面热变形。Zi(tcont)表示tcont作用下抛光垫表面轮廓各点相对高度;Zi表示抛光垫表面轮廓各点的原始高度;集合(ρi,ΔZi(t))i=1,2,…,m表示抛光垫表面热变形的样本数据。
将式(24)带入到式(27),可以得到
ΔZi(tcont)=zi-zli
式中,zi表示热场调控参数tcont作用下抛光垫表面轮廓各点相对高度测量结果;zli表示抛光垫表面原始轮廓的测量结果。式(24)中的误差项δij和ηij通过数据相减予以消除,因此,热变形的测量精度主要由激光位移传感器精度决定,传感器重复精度为0.02 μm,抛光垫表面轮廓测量值在1~30 μm之间,根据计量1/3原则,传感器LK-H020满足精度要求。
设FPV和FRMS分别表示抛光垫表面热变形峰谷值以及平均值,则
FPV=maxi=1,2,..m(ΔZi(tcont))-mini=1,2,..m(ΔZi(tcont))
FRMS=∑(ΔZi(tcont)-ΔZ0(tcont))2m,i=1,2,3,…,m
式中,ΔZ0(tcont)表示参考高度,ΔZ0(tcont)=∑i=1mΔZi(tcont)/m。在参数tcont为16、17、18、19 ℃时,分别对抛光垫表面热变形进行测量,测量基本参数设定如表3所示,各组实验参数如表4所示。
平面光学元件抛光实验方案如图11所示,光学元件放置在抛光垫表面,转台C轴带动抛光垫进行匀速转速,S轴带动光学元件转动,抛光液循环系统提供均匀分布的抛光液。抛光加工的实验参数如表5所示,分别在参数tcont为16 ℃、18 ℃和20 ℃时对光学元件进行抛光加工(每种参数下元件加工3次),采用干涉仪对元件加工表面面形精度进行测量,每次加工时间为8 h,9组加工实验的参数设定如表6所示。
金属锡抛光垫表面轮廓在不同参数tcont下的热变形测量结果如图12所示。当tcont=19 ℃时,在径向距ρ=600 mm处的热变形最小wρ=600≈0,随着ρ减小,抛光垫表面热变形缓慢增加,从ρ=600 mm到300 mm处抛光垫表面热变形w从0增加到了-2.2 μm;在ρ=300 mm到100 mm的位置,抛光垫表面热变形w基本维持在-2.2 μm。tcont= 18 ℃时,ρ = 600 mm位置处的抛光垫表面热变形最小,wρ=600≈0,从ρ=600 mm到300 mm处抛光垫表面热变形w增加速率较tcont=19 ℃时的速率有所提高,从0增加到了-6.2 μm;在ρ= 300 mm到100 mm的位置,抛光垫表面热变形w基本维持在-6.2 μm。tcont= 17 ℃时抛光盘表面的变化规律与tcont=18 ℃时类似,都是在ρ = 600 mm到300 mm处,抛光垫表面热变形w快速增加,在ρ = 300 mm到100 mm的位置,抛光垫表面热变形w基本维持不变(-11.1 μm);当tcont=16 ℃,抛光垫表面热变形随着ρ的减小持续增加,最大热变形在ρ=100 mm处,此时热变形wρ=100=-16.9 μm。整体上,当tcont= 16 ℃ ~ 19 ℃之间时,抛光垫表面产生下凹形状的热变形,且温度越低,变形程度越大。tcont在各温度下,抛光垫表面的热变形最大值和平均值如表7所示。
抛光垫热场调控热变形实验及仿真结果如图13所示,首先,对于ANSYS仿真结果,tcont从16到19 ℃,热变形最大值呈线性变化(24.8 μm降低到3.6 μm),同样热变形平均值也呈现线性变化(从7.4 μm降低到1.3 μm);抛光垫热场调控实验也有类似结论,当tcont从16到19 ℃,抛光垫表面热变形最大值呈线性降低(16.9 μm降低到2.2 μm),热变形平均值也呈现线性变化(从12.5 μm降低到2.0 μm),仿真结果与实验结果的变化趋势一致。但是,仿真与实验结果的数值存在一定偏差,参数tcont不同数值下,热变形平均值的偏差分别为40.8 %(16 ℃)、59.1 %(17 ℃)、60.0 %(18 ℃)以及35 %(19 ℃),最大值的偏差分别为 -46.7 %(16 ℃)、3.6 %(17℃)、-16.1 %(18 ℃)以及-63.6 %(19 ℃)。因此仿真模型还不能精确预测抛光垫表面的热变形量,偏差在-63.6 % ~ 60 %之间。
产生上述误差的可能原因有:1)简化了ANSYS仿真模型,包括复合抛光盘内部螺纹孔、倒角以及抛光垫表面沟槽等结构,以提高计算效率;2)复合抛光盘实际约束条件和仿真约束条件可能有所不同。
根据式(16),设抛光盘热变形系数为θaver,热变形最大值系数为θmax,则进一步化简可得
w=θaver(tinter-tcont)wmax=θmax(tinter-tcont)θaver=a664D1-ρ2a25+μ1+μ-ρ2a2∑i=15βiθmax=a664D5+μ1+μ∑i=15βi
根据式(31)可知,抛光垫表面热变形的平均值与最大值和热场参数呈线性关系,综上所述,本文所构建的抛光垫表面热变形方程、ANSYS力学模型以及实验结果具备趋势一致性,即随着tcont的提高,抛光盘表面热变形的幅度减小。
最后,利用9组平面元件加工实验对热场调控的效果进行验证,实验结果如表8和图14所示,当tcont=16 ℃时,光学元件加工表面面形精度最差,3次加工后平面元件面形精度峰谷值即PV值分别是1.03λ、0.83λ和0.90λ,均方根值即RMS值分别是0.20λ、0.18λ和0.20λ,三次加工结果面形精度的PV平均值为0.92λ,RMS平均值为0.19λ。当tcont=18 ℃,平面元件的面形精度最优,3次加工元件面形精度PV值分别是0.75λ、0.68λ和0.80λ,RMS值分别是0.16λ、0.15λ和0.18λ,PV平均值为0.74λ,RMS平均值为0.16λ。当tcont= 20 ℃时,元件加工精度有所降低,此时元件面形的PV平均值为0.81λ,RMS平均值为0.18λ,比18 ℃时的加工精度更低,但优于16 ℃的加工结果。根据上述分析可知,改变参数tcont的数值,可以实现元件面形精度优化,当tcont=16 ℃ 时,加工结果最差,当tcont=18 ℃ 时,加工结果最好,面形精度PV值平均提升20%,RMS值平均提升15%。单次实验下,元件面形精度PV和RMS值最大提升为34%和25%。
论文提出一种金属锡盘抛光垫表面轮廓热场调整的方法,并对抛光盘表面热变形量进行了数学建模、有限元仿真以及实验验证,得到结论如下:
1)基于多金属热变形效应建立了抛光垫表面形貌的可控热变形预测模型;
2)建立抛光垫热场调控的ANSYS有限元模型,通过实验对模型进行了验证,在tcont从16 ℃到19 ℃区间,抛光盘热变形的有限元分析结果与实验结果的变化趋势一致。
3)抛光垫热场调控系统在tcont=16 ℃时产生的热变形最大,最大变形量为16.9 μm,平均变形量为12.5 μm;在tcont=19 ℃时产生的热变形最小,最大变形量为2.2 μm,平均变形量为2 μm。
4)利用参数tcont的调整,可以提高元件表面的加工精度,当tcont= 18 ℃ 时,平面光学元件抛光加工精度最高,和tcont= 20 ℃以及tcont= 16 ℃时相比,面形精度PV值平均提升20%,RMS值平均提升15%。
5)根据对比分析,抛光垫表面热变形的数学模型和ANSYS的仿真分析还不能准确预测具体热变形的数值,精确的模型分析将在后续研究进行开展。

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doi: 10.3788/gzxb20265502.0222004
  • 接收时间:2025-09-01
  • 首发时间:2026-10-10
  • 出版时间:2026-02-25
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  • 收稿日期:2025-09-01
  • 录用日期:2025-09-28
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    1北京石油化工学院 机械工程学院, 北京 102627
    2西安交通大学 机械工程学院, 西安 710049

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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
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