不等螺旋角立铣刀瞬时铣削力模型与验证

Instantaneous Milling Force Model and Verification of Unequal Helix Angle End Mill

随着航空航天轻量化趋势的迫切需求,铣削是框架类弱刚度零部件不可或缺的加工方法,然而铣削过程瞬时力变化导致薄壁结构件等弱刚度工件的颤振产生加工变形是其技术瓶颈。而立铣刀不等分齿间角和螺旋角已被证实是抑制颤振的有效方法。但切削力变化是诱发工艺系统颤振的本源,不等螺旋角立铣刀铣削弱刚度结构件力学行为尚未完善。基于此,建立了不等螺旋角立铣刀瞬时铣削力数学模型。首先,分析了不等螺旋角周向平面化下角度位置关系,研究了切削刃之间的轴向时变特性对任意轴向位置瞬时切削厚度的影响关系,建立了不等分齿间角微元体的力模型并轴向积分后得到单刃瞬时切削力模型。其次,分析了不等螺旋角切削刃在切削域中的参与情况,并提出了多刃同时切削时多窗口函数叠加的铣削力线性预测方法。进一步的,采用了线性回归后的斜切变换方法进行系数标定,得到了基于铣削斜变化下的系数预测方法。最后,开展了传统立铣刀与不等螺旋角立铣刀干式铣削Ti-6Al-4V验证性实验。结果表明,线性回归方法下的传统立铣刀数值解与测量值在进给方向Fy平均误差为1.17%,切削表面法向Fx平均误差为2.09%。铣削斜切变换方法下不等螺旋角立铣刀得到的Fy平均误差为0.13%,相比于线性回归方法预测精度提高了6.36%。不等螺旋角导致切削刃之间具备的轴向时变特性,是导致了力信号周期性改变,抑制颤振的根本原因。

With the urgent demand for lightweight trends in aerospace,milling is an indispensable processing method for weak stiffness components such as frames.However,the instantaneous force changes during the milling process lead to vibration and machining deformation of weak stiffness components such as thin-walled structural components,which is the technical bottleneck.The unequal division of pitch and helix angle for end mills has been proven to be an effective method for suppressing chatter.However,changes in cutting force are the root cause of inducing process system chatter,and the mechanical behavior of milling weak stiffness structural components with unequal helix angle end mills has not yet been improved.Based on this,a mathematical model for instantaneous milling force of unequal helix angle end mills is established.Firstly,the angle position relationship under circumferential planarization of unequal helix angles is analyzed,and the influence of axial time-varying characteristics between cutting edges on the instantaneous cutting thickness at any axial position is studied.A force model of micro elements with unequal pitch is established and integrated axially to obtain a single edge instantaneous cutting force model.Secondly,the participation of unequal helix angle cutting edges in the cutting domain is analyzed,and a linear prediction method for milling force is proposed based on the superposition of multiple window functions when multiple cutting edges are simultaneously cut.Furthermore,the oblique transformation method after linear regression is used for coefficient calibration,a coefficient prediction method based on milling oblique transformation is obtained.Finally,validation experiments are conducted on dry milling of Ti-6Al-4V using a traditional end mill and an unequal helix angle end mill.The results show that under the linear regression method,the average error between the numerical solution of the traditional end milling cutter and the measured value in the feed direction Fy is 1.17%,and the average error in the cutting surface normal direction Fx is 2.09%.The average error of Fy obtained by the unequal helix angle end milling cutter using the milling oblique transformation method is 0.13%,which improves the prediction accuracy by 6.36%compared to the linear regression method.The axial time-varying characteristics between cutting edges caused by unequal helix angles are the fundamental reason for periodic changes in force signals and suppression of chatter.