张跃敏, 郭海运, 贾贺威,等.超声椭圆振动铣削钛合金的稳定性研究[J].河南理工大学学报（自然科学版）,doi:10.16186/j.cnki.1673-9787.2022050038

ZHANG Y M, GUO H Y, JIA H W, et al.Stability study on ultrasonic elliptical vibration milling titanium alloy[J].Journal of Henan Polytechnic University(Natural Science) ,doi:10.16186/j.cnki.1673-9787.2022050038

超声椭圆振动铣削钛合金的稳定性研究（网络首发）

张跃敏, 郭海运, 贾贺威, 王晓博

河南理工大学 机械与动力工程学院，河南 焦作，454000

摘要:为了实现无颤振铣削钛合金材料，采用超声椭圆振动铣削的加工方法并进行稳定性分析。由于超声 椭圆振动铣削呈现出更高频次的断续加工特性，为了求出真实的瞬态切厚，根据仿真分析超声椭圆振动铣削 的刀尖轨迹，提出坐标法建立窗口函数预判求解刀齿的瞬时切厚。利用非线性周期函数的线性化理论，建 立超声椭圆振动铣削的动力学模型，通过全离散法求解动力学模型，利用Floquet定理获得不同转速所对 应的临界切深，构建超声椭圆振动铣削和普通铣削系统的稳定性预测曲线，并通过颤振试验进行验证和分 析。结果表明：随着转速增加，超声椭圆振动铣削系统的轴向切深极限值和稳定性区域在不断增加；当转 速小于3 000 r/min时，超声椭圆振动铣削无颤振加工的轴向切深极限值比普通铣削提高了 50%。数值仿真 结果与试验结果较好吻合，验证了理论模型和预测稳定性曲线是有效和可靠的。

关键词:稳定性分析;超声椭圆振动铣削;坐标法;钛合金

中图分类号: TG54

doi:10.16186/j.cnki.1673-9787.2022050038

基金项目:国家自然科学基金资助项目（52005164）；河南省高等学校重点科研计划项目（22A416005）；河南省高校基本科研业务费专项资金资助项目（NSFRF210422）；河南理 工大学博士基金资助项目（B2018-20）

收稿日期:2022-05-12

修回日期:2022-10-09

网络首发日期:2022-11-07

Stability study on ultrasonic elliptical vibration milling titanium alloy（Online）

ZHANG Yuemin, GUO Haiyun, JIA Hewei, WANG Xiaobo

School of Mechanical and Power Engineering，Henan Polytechnic University，Jiaozuo 454000，Henan，China

Abstract:In order to realize no chatter in milling titanium alloy materials， ultrasonic elliptical vibration milling was put forth and studied on stability analysis. Because ultrasonic elliptical vibration milling （UEVM） system had a characteristic of high frequency intermittent cutting， it was difficult to achieve instantaneous chip thickness. The motion trajectories of tool tip were simulated and analyzed in UEVM system. According to trajectory character of tool tip， the coordinate method was put forth for establishing window function to predict and solve instantaneous chip thickness in UEVM system. Then using linear theory of nonlinear periodic function， the dynamic model of UEVM had been established and solved by full-discretization method. The critical cutting depth corresponding to different rotational speeds was obtained by the Floquet theorem．The stability prediction lobes diagrams were constructed. Final， stability tests of UEVM had been carried out on titanium alloy workpieces. The experimental results showed that the limit values of axial cutting depth and the stability areas of UEVM were increasing with the rising of spindle speed. When the speed was less than 3 000 r/min， the axial cutting depth of UEVM under no chatter was up to 50% higher than that of ordinary milling. The experimental results coincided with the numerical simulation. It showed that the proposed window functi.on was correct， the theoretical model was valid and the prediction stability curves was feasible and reliable.

Key words:stability analysis;ultrasonic elliptical vibration milling;coordinate method;titanium alloy

CLC: TG54