Mechanical dynamics modeling and analysis of the special machine for vertical inner cavity
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摘要: 针对立式四轴舱体内腔加工专机,基于动态子结构法进行了机械动力学建模。求解了专机动结合部的滚珠丝杠副和直线导轨副的动态刚度特性。由建立的动力学模型分析整机的固有模态,应用解析法求解整机的固有频率。应用有限元软件建立专机有限元模型,求解结合部刚性接触与设定了动态刚度性的整机固有频率与振型及谐响应分析结果。结果显示建立的含动态刚度的动力学模型能够有效镜像专机动力学特性,可应用于专机的动力分析与数字孪生虚拟样机研究。Abstract: For the vertical four-axis inner cavity machining special machine,the mechanical dynamics modeling is carried out based on the dynamic sub-structure method. The dynamic stiffness characteristics of the ball screw pair and linear guide pair of the special motorized joint are solved. The natural mode of the whole machine is analyzed by the established dynamic mode, and the natural frequency is solved by the analytical method. The finite element mode of the machine is established by the finite element software, and the analysis results of the natural frequency, mode shape and harmonic response of the whole machine with the rigid contact of the joint and the dynamic stiffness are set. The results show that the established dynamic model with dynamic stiffness can effectively mirror the dynamic characteristics of the machine, and can be applied to the dynamic analysis of the machine and the research of the digital twin virtual prototype.
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表 1 专机刚性结合部刚度
刚性结合部 线刚度/(N/m)、角刚度/(N·m/rad) 床身与地面 $ {K}_{y}^{\text{①}}=7.642\times {10}^{8} $、$ {K}_{\theta {\textit{z}}}^{\text{①}}=3.629\times {10}^{7} $、$ {K}_{\theta x}^{\text{①}}=5.473\times {10}^{7} $ 滑枕与主轴 $ {K}_{x}^{\text{④}}=7.218\times {10}^{7} $、$ {K}_{y}^{\text{④}}=2.512\times {10}^{8} $、$ {K}_{{\textit{z}}}^{\text{④}}=2.512\times {10}^{8} $
$ {K}_{\theta x}^{\text{④}}=4.538\times {10}^{7} $、$ {K}_{\theta {\textit{z}}}^{\text{④}}=4.341\times {10}^{7} $表 2 机床子结构的质量及转动惯量
子结构 质量/kg 转动惯量/(kg·m²) 床身 $ {m_1} = 6.316 \times {10^3} $ $ {I_{{\textit{z}}1}} = 6.37 \times {10^3} $、$ {I_{x1}} = 4.43 \times {10^3} $ 立柱 $ {m_2} = 834 $ $ {I_{x2}} = 77 $、$ {I_{{\textit{z}}2}} = 180 $ 滑枕 $ {m_3} = 275 $ $ {I_{y3}} = 46 $、$ {I_{{\textit{z}}3}} = 13 $ 主轴 $ {m_4} = 213 $ $ {I_{x4}} = 109 $、$ {I_{{\textit{z}}4}} = 99 $ 工作台 $ {m_5} = 2.052 \times {10^3} $ $ {I_{x5}} = 191 $、$ {I_{{\textit{z}}5}} = 238 $ 表 3 有限元仿真部件材料属性设置
部件 材料 密度/(kg/m3) 弹性模量/GPa 泊松比 床身、立柱 HT200 7 340 120 0.25 滑枕、主轴、
工作台Q235 7 850 200 0.3 表 4 含动结合部刚度求解的专机固有频率
固有频率/Hz 一阶$ {f_1} $ 二阶$ {f_2} $ 三阶$ {f_3} $ 四阶$ {f_4} $ 理论方法(基准) 35.1 36.9 76.4 73.7 刚性接触 40.2 42.9 90.6 91.7 设置动结合部刚性的
有限元法34.2 38.2 78.6 79.4 刚性接触与基准
相比误差14.5% 16.3% 18.6% 24.4% 设置动结合部刚性的有限元法与基准相比误差 2.6% 3.5% 2.9% 7.7% -
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