<p>Aspheric optical elements play a crucial role in optical engineering, owing to their distinctive optical properties. The grinding process, crucial in the manufacturing of aspheric components, significantly impacts the performance of these components through its machining accuracy. In this paper, based on the theory of multi-body kinematics, the motion error model of a three-degree-of-freedom ultra-precision grinder is established. The workpiece is processed using grating parallel grinding method, with an analysis of the principal errors in parallel grinding. Additionally, considering the motion error of the machine tool and the principle error of parallel grinding, a prediction model for grinding accuracy is developed. This model establishes a correlation between the machine tool’s motion error and the resultant surface shape of the workpiece. Validation of this model is achieved through grinding experiments conducted on aspheric optical elements. The simulation forecasts a PV value of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="170_2025_15964_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">$9.7\;\mu m$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>9.7</mn> <mspace width="0.277778em" /> <mi>μ</mi> <mi>m</mi> </mrow> </math></EquationSource> </InlineEquation> for the workpiece surface type, while the actual machined workpiece surface type exhibits a PV value of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="170_2025_15964_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">$11.71\;\mu m$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>11.71</mn> <mspace width="0.277778em" /> <mi>μ</mi> <mi>m</mi> </mrow> </math></EquationSource> </InlineEquation>, resulting in a relative error of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="170_2025_15964_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">$17.2\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>17.2</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>. These findings confirm the accuracy of the prediction model for grinding accuracy and extend its potential engineering applications in aerospace and other fields.</p>

Study on the prediction model of form accuracy during grinding of aspheric optical components

期刊论文
发表日期：

2025年6月30日

查看全文

Ri Pan,
Yimin Zheng,
Chunfu Hu,
Zhenzhong Wang,
Peng Gao

摘要

Aspheric optical elements play a crucial role in optical engineering, owing to their distinctive optical properties. The grinding process, crucial in the manufacturing of aspheric components, significantly impacts the performance of these components through its machining accuracy. In this paper, based on the theory of multi-body kinematics, the motion error model of a three-degree-of-freedom ultra-precision grinder is established. The workpiece is processed using grating parallel grinding method, with an analysis of the principal errors in parallel grinding. Additionally, considering the motion error of the machine tool and the principle error of parallel grinding, a prediction model for grinding accuracy is developed. This model establishes a correlation between the machine tool’s motion error and the resultant surface shape of the workpiece. Validation of this model is achieved through grinding experiments conducted on aspheric optical elements. The simulation forecasts a PV value of $9.7\;\mu m$ $9.7 μ m$ for the workpiece surface type, while the actual machined workpiece surface type exhibits a PV value of $11.71\;\mu m$ $11.71 μ m$ , resulting in a relative error of $17.2\%$ $17.2 %$ . These findings confirm the accuracy of the prediction model for grinding accuracy and extend its potential engineering applications in aerospace and other fields.