面向车削颤振抑制的多重阻尼器优化设计

Optimization of multiple tuned mass dampers for chatter suppression in turning

在相同质量比下,多重阻尼器相对单阻尼器具有抑振频带更宽及效果更佳等一系列优点。以往针对阻尼器的参数优化大多采取H∞或H2方法,即最小化主结构振动幅值的最大值或有效值。然而机床加工中发生的颤振是一种特殊的自激振动;对车削而言,无颤振的临界切深仅由刀具-工件相对频响函数的负实部决定。通过应用多重阻尼器于机械加工中再生颤振的抑制,研究以获取最大稳定无颤振切深为目的阻尼器设计优化路线。在建立多重阻尼器抑制主结构目标函数,即最大化刀尖频响函数负实部最小值的基础上,构造minimax方法对多重阻尼器的刚度及阻尼进行优化。以抑制车床夹具某一主模态为例,结合实验模态分析,采用该方法调制阻尼器,并和以往的优化方法进行对比。切削实验表明,该优化方法能进一步提升多重阻尼器的颤振抑制性能;相对H∞优化方法,该方法可提高无颤振临界切深52%。

Multiple tuned mass dampers （TMDs） are superior to the single TMD with the same mass in the bandwidth and effectiveness for vibration control, and the most adopted optimization methods for TMDs are H∞or H2 （i. e. minimization of the amplitude or root mean squared value of the vibration）. However, the chatter vibration in the machine tool is a special self- excited problem. Especially for turning, the chatter-free depth of cut is only determined by the negative real part of the rela- tive frequency response function （FRF） between the tool and workpiece. The objective function of multiple TMDs damping the primary structure was formulated （i. e. maximizing the most negative point of tool point FRF）, and the minimax approach was employed to optimize the stiffness and damping of each TMD. The advantage of the proposed method was validated by tuning three TMDs on a specially designed fixture of a turning machine after performing the modal test. The cutting tests demonstrate that the tuning method can further increase the chatter suppression performance of multiple TMDs, and the chatter free depth of cut can be increased 52 % more than the H∞ method.