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针对普通圆锯片及基体开槽圆锯片的振动响应问题,首次引入集中质量法建立了圆锯片无阻尼多自由度弹簧-质量系统模型。将开槽等效为去除槽分布对应区域内的弯曲弹簧,分别构造了普通圆锯片、基体开径向槽以及周向槽三类圆锯片振动系统模型的质量矩阵与刚度矩阵,并进行了简谐激励响应分析。采用振幅强度因子作为衡量锯片振动强度的指标,通过求解获得了振幅强度因子与频率关系的幅频响应特性曲线,将计算结果同有限元法的结果进行对比分析,结果表明:当峰值对应频率在0~750Hz范围内时,二者的一致性较好;当峰值对应频率大于750Hz时,开始出现较大偏差,验证了集中质量法用于计算圆锯片结构低频固有特性的正确性。本文研究结果对于求解存在几何缺陷的连续体弹性薄板的振动响应具有一定的参考价值。
Aimed at the vibration response of circular saw blades and grooving circular saw blades, an un-damped multi-degree-of-freedom spring-mass system model of circular saw was established for the first time by introducing mass-concentration method. The slotting is equivalent to removing the bending spring in the corresponding region of the slot distribution, and the mass matrix and stiffness matrix of the vibration system model of three kinds of circular saw blades, the radial groove and the circumferential groove are constructed and carried out respectively Simple harmonic excitation response analysis. By using the amplitude intensity factor as an index to measure the vibration intensity of the saw blade, the amplitude-frequency response characteristic curve of the amplitude intensity factor and the frequency is obtained. The calculated results are compared with the results of the finite element method. The results show that when the peak frequency In the range of 0 ~ 750Hz, the consistency between the two is good. When the peak corresponding frequency is greater than 750Hz, large deviation starts to occur, which verifies the validity of the mass-concentration method in calculating the inherent characteristics of low frequency of circular saw blade structure. The results of this paper have certain reference value for solving the vibration response of continuous thin slabs with geometrical defects.