由于薄壁工件刚度较低，在加工过程中极易出现较强的强迫振动，因此导致工件加工质量降低，并进一步限制了工艺参数的选择。为求解薄壁工件的强迫振动响应并对其加以抑制，该文针对圆角立铣刀，基于力学方法建立了铣削力模型，通过实验标定切削力系数；基于实验模态分析方法，对薄壁工件的动态特性进行分析，得到刀具-工件振动系统的传递函数和模态参数；基于直接时域求解方法得出了薄壁结构受切削力激励产生的强迫振动响应（forced vibration response，FVR），并以稳态响应最大振幅为判断依据描述工件的振动强度。最后通过仿真得出了刀尖半径对强迫振动响应具有抑制作用的结论。
Strong forced vibrations can easily occur while milling thin-walled workpieces because of their low stiffness. Such vibrations not only reduce the product quality, but also limit the choose of the machining parameters. The forced vibrations of thin-walled workpieces during milling were investigated by using an R-end milling cutter to reduce the cutting forces and the cutting coefficients in cutting experiments. The dynamics of the thin-walled workpiece were analyzed based on modal experiments to obtain the transfer function and modal parameters of the tool-workpiece system. The forced vibration response was then predicted using a time-domain method. The simulations indicate that a proper nose radius can suppress the forced vibration response.
[1] 汪通悦, 何宁, 李亮. 薄壁零件铣削加工的振动模型[J]. 机械工程学报, 2007, 43(8):22-25. WANG T Y, HE N, LI L. Vibration model in milling of thin-walled components[J]. Chinese Journal of Mechanical Engineering, 2007, 43(8):22-25. (in Chinese)
[2] KO T J, KIM H S, LEE S S. Selection of the machining inclination angle in high-speed ball end milling[J]. The International Journal of Advanced Manufacturing Technology, 2001, 17(3):163-170.
[3] MUNOA J, BEUDAERT X, DOMBOVARI Z, et al. Chatter suppression techniques in metal cutting[J]. CIRP Annals, 2016, 65(2):785-808.
[4] KIVANC E B, BUDAK E. Structural modeling of end mills for form error and stability analysis[J]. International Journal of Machine Tools and Manufacture, 2004, 44(11):1151-1161.
[5] TSAI J S, LIAO C L. Finite-element modeling of static surface errors in the peripheral milling of thin-walled workpieces[J]. Journal of Materials Processing Technology, 1999, 94(2-3):235-246.
[6] TANG A J, LIU Z Q. Deformations of thin-walled plate due to static end milling force[J]. Journal of Materials Processing Technology, 2008, 206(1-3):345-351.
[7] 罗忠, 王宇, 孙宁, 等. 不同边界条件下旋转薄壁短圆柱壳的强迫振动响应计算[J]. 机械工程学报, 2015, 51(9):64-72. LUO Z, WANG Y, SUN N, et al. Forced vibration response calculation of rotating short thin cylindrical shells for various boundary conditions[J]. Journal of Mechanical Engineering, 2015, 51(9):64-72. (in Chinese)
[8] GAO Y Y, MA J W, JIA Z Y, et al. Tool path planning and machining deformation compensation in high-speed milling for difficult-to-machine material thin-walled parts with curved surface[J]. The International Journal of Advanced Manufacturing Technology, 2016, 84(9-12):1757-1767.
[9] RIVIÈRE-LORPHÈVRE E, HUYNH H N, VERLINDEN O. Influence of the time step selection on dynamic simulation of milling operation[J]. The International Journal of Advanced Manufacturing Technology, 2018, 95(9-12):4497-4512.
[10] ALTINTAS Y. Manufacturing automation:Metal cutting mechanics, machine tool vibrations, and CNC design[M]. 2nd ed. Cambridge:Cambridge University Press, 2012.
[11] TUYSUZ O, ALTINTAS Y. Frequency domain updating of thin-walled workpiece dynamics using reduced order substructuring method in machining[J]. Journal of Manufacturing Science and Engineering, 2017, 139(7):071013.
[12] DING Y, ZHU L D. Investigation on chatter stability of thin-walled parts considering its flexibility based on finite element analysis[J]. The International Journal of Advanced Manufacturing Technology, 2018, 94(9-12):3173-3187.
