关键词：锥度球头刀；钛合金TC4;四轴铣削;残余应力；逆向辨识;离散度中图分类号：V261.2DOI：10.3969/j.issn.1004-132X.2025.04.014 开放科学（资源服务）标识码（OSID）：

Inverse Solution for TC4 Residual Stress Gradient Distribution in Four-axis Milling with Tapered Ball-end Cutters

ZHOU Jinhua1，2 * QI Qi1'² REN Junxue1² ZHAN Mei1，2 1.Key Laboratory of High Performance Manufacturing for Aero Engine，Ministry of Industry and Information Technology，Northwestern Polytechnical University，Xi'an，710072 2.Engineering Research Center of Advanced Manufacturing Technology for Aero Engine， Ministry of Education，Northwestern Polytechnical University，Xi'an，710072

Abstract： The internal and external profile finishing of the metal reinforcing edges of the leading edge of large composite fan blades for commercial aero-engines was accomplished by four-axis milling with a customized taper bal-end cutter，and the machining residual stresses introduced at this stage often caused excessive bending and torsional deformations leading to dimensional overshoots of the parts. For the four-axis milling of titanium alloy TC4 with taper ball-end cutter，an inverse identification method of miling residual stress gradient distribution was proposed based on the deformation tests of thin plate machining herein. The hyperbolic tangent models were used to parametrically characterize the miling residual stress gradient distribution，and the solution of the residual stress gradient distribution was converted into the inverse solution of two pending coeficients k and ω . The model coefficient k was determined by testing the residual stress on the machined surfaces of the titanium alloy specimen blocks，and the model coefficient ω was inversely solved by testing the bending deformation deflection of milled titanium ally thin plates，then the residual stress gradient distribution curve was determined.Four groups of titanium alloy TC4 test block miling validation experiments were carried out，and the test results show that the average prediction accuracy of the miling residual stress gradient distribution is as high as 99.35% . Compared with the traditional X-ray test method，the proposed method avoids the use of electrolytic corrosion stripping to test the subsurface residual stresses， and also takes into full consideration the non-uniformity of the distribution of milling residual stresses on the machined surfaces，namely the problem of the dispersion of milling residual stresses.

Key words： tapered ball-end cutter； titanium alloy TC4； four-axis milling；residual stress； re-verse identification；dispersion

0 引言

大型复合材料风扇叶片是我国大涵道比涡扇发动机实现结构创新与技术跨越的关键，其减重增效对提高发动机推重比和服役寿命极为重要。

树脂基复合材料风扇叶片与钛合金叶片相比，具有质量小、效率高、噪声低、燃油消耗率低、抗颤振性能和损伤容限能力优异等特点。其不足之处在于，当叶片高速旋转时进气边易分层开胶、抗冲击和抗鸟撞能力严重不足，在风扇叶片前缘部位必须采用金属加强边结构以提高其抗冲击、抗鸟撞以及抗腐蚀性能。西北工业大学采用多轴精密数控加工技术在国内率先完成了钛合金前缘金属加强边的精密制造，其内外型面精加工采用锥度球头刀四轴铣削加工方式完成[]。该零件属于大型超薄壁V形结构，锥度球头刀四轴精加工产生的残余应力引起了严重的弯曲、扭转变形，从而造成尺寸超差，因此，锥度球头刀铣削加工钛合金TC4残余应力沿深度方向的梯度分布规律研究成为急需突破的技术瓶颈之一。

准确获取加工残余应力梯度分布是有效控制薄壁结构加工残余应力变形的基础。残余应力的测量方法包括有损检测和无损检测两种。有损检测方法采用半破坏性或全破坏性检测方法去除试样材料，并根据该区域的位移或应变获得残余应力。GHAEDAMINI等[2]采用钻孔法和环芯法估算复合材料的残余应力，结果表明，环芯法比钻孔法至少能多释放 17% 的应力。……