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）,2024,43(4):117-125.

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) ,2024,43(4):117-125.

超声椭圆振动铣削钛合金的稳定性研究

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:超声椭圆振动铣削是一种能够降低切削力、改善工件表面质量、抑制颤振、提高加工效率等的切削加工技术。 目的 为了实现无颤振铣削钛合金材料， 方法 采用超声椭圆振动铣削加工技术，并对加工系统的稳定性展开研究。超声椭圆振动铣削在加工过程中具有高频断续的加工特性，瞬态切厚模型与普通铣削不同。为了求出该系统的真实瞬态切厚，利用MATLAB软件仿真求解超声椭圆振动铣削的刀尖运动方程并分析刀尖运动轨迹，采用坐标法建立窗口函数，预判求解刀齿的瞬时切厚。在此基础上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。通过全离散法求解系统状态转移矩阵的特征值，利用Floquet定理判定系统的稳定性，获得不同转速对应的临界切深，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 结果表明：超声椭圆振动铣削系统随着转速增加，系统的轴向切深极限值和稳定性区域不断增加；转速达到6 000 r/min时，轴向切深极限值急剧增加；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%。 结论 数值仿真结果与试验结果吻合较好，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

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:2022/09/29

出版日期:2024/07/15

Stability study on ultrasonic elliptical vibration milling titanium alloy

ZHANG Yuemin, GUO Haiyun, JIA Hewei, WANG Xiaobo

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

Abstract:Ultrasonic elliptical vibration milling（UEVM） is a good machining technique of reducing cutting force，improving workpiece surface quality，restraining chatter and increasing product efficiency. Objectives In order to realize no chatter in milling titanium alloy materials，  Methods the method of UEVM was put forth and studied on system stability analysis.The UEVM system had a characteristic of high frequency intermittent cutting，the modal of instantaneous chip thickness was different to ordinary milling.The motion formula of tool tip were simulated by MATLAB software and the motion trajectories were analyzed in UEVM system for solving the true instantaneous chip thickness.According to the 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，by using linear theory of nonlinear periodic function，the dynamic model of UEVM had been established.The eigenvalues of the transition matrix were solved by full-discretization method.The system stability was predicted and critical cutting depth corresponding to different rotational speeds was obtained by the Floquet theorem．The stability prediction curves of UEVM system and ordinary milling system were constructed，and the chatter tests had been carried out to verify and analyze the curves.  Results The limit values of axial cutting depth and the stability areas of UEVM were increasing with the rising of spindle speed.When the speed reached 6 000 r/min，the axial cutting depth of UEVM was increasing sharply.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.  Conclusions The experimental results coincided with the numerical simulation.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