基于相位迁移和误差干涉原理提高齿轮齿距加工精度

The ultra-precision gear has important application value in precision machinery, defense, aerospace and other fields, and the bottleneck of improvement of its manufacturing accuracy is the refining technique of the indexing system of grinding equipment and ultra-precision grinding technology. The pitch processing method of the ultra-precision gear by making the original indexing error curve interfere with its phase-transfer error curve was proposed and was applied to the non-uniform regrinding to improve the pitch processing accuracy of ultra-precision gear. Based on analyzing the extracting method of the original indexing error curve and its characteristics, the mapping law of the indexing error and the judgment of phase transfer were discussed. The mathematical model of describing the mapping relationship between the minimum pitch deviations and the angle of phase transfer, the depth of the error interference, the yield coefficient of the supporting work piece and other variables was established. The internal connection of the pitch processing accuracy, error reflection rules and process matching were revealed, and the strategy of obtaining the smaller single pitch deviation and total cumulative pitch deviation and its implementation method in the machine were probed. The research target is to strive to break through in precision construction of the originalindexing error curve, the non-uniform regrinding theory, the precision control technology of the regrinding allowance and other key technologies. The research has important scientific significance and study value for establishing new theory and new technology of ultra-precision gear pitch processing and promotion of the technological level of ultra-precision gears.

超精密齿轮在精密机械、国防、航空航天等领域具有重要应用价值，制约其齿距制造精度提高的瓶颈在于磨齿设备分度系统的精度和齿轮齿距加工工艺。本项目提出基于原始分度误差曲线与其相位迁移误差曲线相干涉的齿距加工方法，并用于二次非均匀磨齿工艺，以提高超精密齿轮的齿距加工精度。在研究原始分度误差曲线的提取方法与特性分析的基础上，研究机床分度系统的误差映射规律与相位迁移判据，建立描述最小齿距偏差与相位迁移角、误差干涉深度、支承工件退让系数等多变量之间映射关系的数学模型，揭示齿距加工精度、误差复映规律及加工工艺匹配之间的内在联系，探索获取较小单一齿距偏差和齿距累积总偏差的策略与在机实现方法，力争在原始分度误差曲线的精确构建、非均匀磨齿的相关理论、二次加工余量的精确控制等关键技术上有所突破。本项研究对于建立超精密齿轮齿距加工的新原理与新的技术手段，提升超精密齿轮的制造技术水平有重要的科学意义与研究价值。

齿轮是机械零件中非常重要的基础件之一，尤其是圆柱渐开线齿轮广泛应用于常规机械、地面交通、船舶、航空航天、兵器、精密机床与仪器等领域。与机床分度精度相关的单个齿距偏差fpt和齿距累积总偏差Fp即是齿轮国家标准GB/T 10095.1-2008中规定的必检项目，也齿轮国际标准ISO1328-1:2013中的默认检查项目。本项目基于相位迁移和误差干涉原理，针对提高齿轮的齿距加工精度开展了机床分度误差传递规律及相位迁移磨齿工艺的研究工作，并取得了如下研究成果：.(1) 采用全闭环测量法对正36面棱体进行了高精度标定，标定的测量不确定达±0.05″；.(2) 采用经过全闭环测量法标定的正36面棱体和相对测量法在机精密提取机床36个均布离散点的系统分度误差曲线，最大分度误差为6.8″；.(3) 通过精密磨齿实验研究磨齿机系统分度误差的传递规律。系统分度误差传递到被加工齿轮后，齿距累积总偏差由2.08μm增大为2.57μm；.(4) 通过实验方法得到了特定工况下机床分度误差传递过程中的不确定为±0.6μm。根据机床原始系统分度误差及磨齿机分度误差传递过程中的不确定度可预测齿轮的齿距加工精度；.(5) 在研究磨齿机系统分度误差提取方法基础上，提出了利用系统分度误差曲线与其相位迁移误差曲线相干涉的相位迁移磨齿工艺；.(6) 采用传统的精密磨齿工艺得到的齿轮试件的齿距累积总偏差为2.57 μm，较系统分度误差增大了约24%；而采用本项目提出的相位迁移磨齿工艺进行精密磨齿，齿轮试件的齿距累积总偏差减小到1.34μm，较系统分度误差减小了约36%。即使考虑齿轮齿距偏差的测量不确定度，试件齿轮的齿距累积总偏差均达到齿轮国家标准(GB/T 10095.1-2008)、德国标准(DIN 3962.1-1978)和国际标准(ISO 1328.1-2013)中的最高等级；. 采用项目提出的相位迁移磨齿工艺可使被加工齿轮的齿距累积加工精度(分度精度)高于磨齿机分度系统的分度精度，这对提高分圆元件(包括：多面棱镜、分度盘、端齿盘、分度齿轮、分度蜗轮、谐波齿轮等)的分度加工精度有重要的现实意义。