Rotational Inertial Characteristics and Dynamic Response of Motorized Spindle Time-Varying Mass System for Magnetic Suspension Milling
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摘要:
针对磁悬浮铣削电主轴在切削加工过程中，因切屑不断进入、离开刀具容屑槽导致系统质量大小和分布不断变化，进而引起系统动力学特性的非线性变化问题. 首先，依据金属连续切削原理求得单个切屑质量，并结合连续梁振动理论，应用有限单元法建立“磁悬浮轴承-电主轴-刀具-切屑”时变质量系统的动力学模型；然后，采用龙格库塔法对系统的运动微分方程进行求解，分析切屑从进入到离开容屑槽的整个过程，切屑质量变化对系统固有频率、振型的影响规律；进而探索由时变切屑质量所引起的旋转惯性载荷、陀螺力矩、切削力、磁悬浮轴承电磁力等激励下的系统振动响应规律；最后，利用MATLAB软件对系统进行仿真求解. 结果表明：切屑质量从0增大到2.08 × 10−5 kg时，系统前三阶临界转速分别下降约2.3、0.7、0.3 r/min，可知时变切屑质量对系统固有特性影响较小；旋转惯性载荷对系统的动态响应有较大影响，尤其是对切削加工点，使切削点的径向振动响应和角向振动响应的幅值出现0～9.7 × 10−7 m和0～2.5 × 10−5 rad不等的增大，还使加工点处径向振动和角向振动平衡位置的偏移距离分别增加约5.1 × 10−7 m和9.3 × 10−6 rad.
Abstract:As chips continuously enter and leave from the tool flute during the cutting process of the motorized spindle for magnetic suspension milling, the size and distribution of the system mass are constantly changing, leading to the nonlinear change of system dynamics characteristics. To address these issues, firstly, the mass of a single chip was calculated based on the principle of continuous metal cutting, and then combined with the theory of continuous beam vibration, the dynamics model of the “magnetic suspension bearing–motorized spindle–tool–chip” time-varying mass system was established by using the finite element method. Secondly, the Runge-Kutta method was used to solve the differential equation of motion of the system, and the influence of chip mass change on the natural frequency and mode shape of the system was analyzed during the entire process covering the chip’s entry into and leave from the tool flute. Then, the vibration response patterns of the system under the excitation of rotational inertial load, gyroscope torque, cutting force, and electromagnetic force of magnetic suspension bearings caused by time-varying chip mass were explored. Finally, the MATLAB software was used to simulate and solve the system. The results show that as the chip mass increases from 0 to 2.08 × 10−5 kg, the system’s first three critical speeds decrease by about 2.3, 0.7, and 0.3 r/min, respectively, indicating that the time-varying chip mass has a small effect on the system’s inherent characteristics. The rotational inertia load has a significant impact on the system’s dynamic response, especially at the cutting point, causing the radial vibration response and angular vibration response amplitudes at the cutting point to increase by 0–9.7 × 10−7 m and 0–2.5 × 10−5 rad, respectively, and it makes the radial vibration and angular vibration equilibrium positions at the cutting point to increase by about 5.1 × 10−7 m and 9.3 × 10−6 rad, respectively.
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图 1 磁悬浮铣削电主轴系统模型示意
Figure 1. System model of motorized spindle for magnetic suspension milling
图 5 “主轴-刀具-切屑”变质量系统的坎贝尔图
Figure 5. Campbell diagram of “spindle–tool–chip” time-varying mass system
图 6 切屑质量对“主轴-刀具-切屑”变质量系统临界转速的影响
Figure 6. Influence of chip quality on critical speed of “spindle–tool–chip” time-varying mass system
图 8 磁悬浮电主轴-刀具-切屑系统振动响应
Figure 8. Vibration response of motorized spindle of magnetic suspension–tool–chip system
图 9 磁悬浮电主轴-刀具-切屑系统切削加工点的振动响应
Figure 9. Vibration response of motorized spindle of magnetic suspension–tool–chip system at cutting point
表 1 磁悬浮电主轴-刀具系统的物理几何参数
Table 1. Physical geometric parameters for motorized spindle of magnetic suspension–tool system
参数 数值 转子总长/mm 500 转子质量/kg 6.427 转子材料 30CrNiMo8 转子弹性模量/Pa 2 × 1011 刀具总长/mm 80 刀具直径/mm 16 刀具材料 W6Mo5Cr4V2Co8 工作转速/（r•min−1） 15000 磁轴承等效刚度/（N•m−1） −2 × 107 
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