Analysis and calculation of dynamic and static thermal characteristics of solid/hollow ball screw
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摘要: 通过对滚珠丝杠系统的热源、热边界条件的确定和计算，分别建立实心/空心滚珠丝杠系统的热稳态仿真分析模型，利用有限元的方法，得到滚珠丝杠系统的热稳态温度场分布，进而利用多场耦合对滚珠丝杠系统进行热结构耦合分析得到实心滚珠丝杠和空心滚珠丝杠的热变形情况，并分析热变形对滚珠丝杠系统的影响；然后分别对实心/空心滚珠丝杠系统进行模态分析和静态分析，分析滚珠丝杠中空后动静态特性的变化和影响，为立式加工中心的优化和改进提供理论依据。Abstract: The thermal steady state simulation analysis models for the solid ball screw system and for the hollow ball screw system were established respectively first based on the determination and computation of the heat source and thermal boundary conditions of the ball screw system. Besides, the finite element method was applied to obtain the thermal steady temperature field distribution. Then, the thermal deformation status of solid ball screw and hollow ball screw was obtained through the thermal structure coupling analysis on the ball screw system with multi-field coupling, and the influence of thermal deformation on the ball screw system was analyzed.After that, the modal analysis and static analysis on the solid/hollow ball screw system were performed respectively to study the changes of the static and dynamic characteristics of the ball screw after being hollowed out. By doing so, it would provide theoretical evidence for the optimization and improvement of the vertical machining center.
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图 1 滚珠丝杠进给系统结构简图
1—上轴承压盖；2—上安装环1；3—上轴承座；4—上轴承组；5—上安装环2；6—滚珠丝杠；7—滚珠丝杠螺母；8—主轴箱；9—立柱；10—下安装压套；11—下安装环1；12—下轴承组；13—下安装环2；14—下轴承压盖。
表 1 滚珠丝杠系统材料参数
参数 SUJ2 45号钢 密度/(kg/m³) 7 830 7 850 弹性模量/Pa 2.08×1011 2.09×1011 泊松比 0.3 0.269 屈服强度/MPa 1 370 355 抗拉强度/MPa 1 617 600 热导率/(W/(m·℃)) 46 50.2 热膨胀系数/(m/℃) 1.2×10−5 1.17×10−5 比热/(J/(kg·℃)) 460 450 
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表 2 实心滚珠丝杠各阶频率及各阶临界速度
阶次 1 2 3 4 5 6 频率/Hz 78.06 208.36 426.64 691.82 995.06 1262.3 临界转速/(r/min) 4 683.6 1 250 1.6 2 559 8.4 4 150 9.2 5 970 3.6 7 573 8
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表 3 空心滚珠丝杠各阶频率及各阶临界速度
阶次 1 2 3 4 5 6 频率/Hz 84.68 220.84 453.32 774.81 1 110.2 1 353 临界转速/(r/min) 5 080.8 1 325 0.4 2 719 9.2 4 648 8.6 66 612 81 180
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