基于模态综合法与动态凝聚的滚珠丝杠进给系统状态空间建模与实验验证

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (13) : 53-59.

论文

杨勇1,张为民2，仇炜谏1，陈盛3

作者信息 +

Establishment and experimental verification of ball screw feed system state space modeling based on modal synthesis and dynamic condensation method

YANG Yong1,ZHANG Wei-Min2，CHOU Weijian1,CHEN Sheng3

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摘要

以往研究中为便于机械传动环节与控制系统的集成建模，常将滚珠丝杠进给系统简化为简单机械模型，其在动态性能精确求解等方面存在不足。针对这一问题，充分考虑滚珠丝杠进给系统的结构柔性以及丝杠螺母副的耦合特性，首先构建滚珠丝杠进给系统多柔体动力学模型；在此基础上，综合模态综合法和动态凝聚法，对进给系统有效简化动力学信息准确提取，加快模型降阶收敛和凝聚自由度响应求解速度，推导得到滚珠丝杠进给系统的状态空间缩聚模型。基于内置传感器信号的动态性能试验测试，对模型的正确性进行验证，其一阶固有频率计算误差为5.54%，实验和仿真计算得到的输入扭矩与输出转速间的频响曲线在一阶频率处极点坐标分别为32.83dB和35.16dB。本文研究为实现滚珠丝杠进给系统与伺服控制系统的高效高精度集成建模提供了重要的理论基础和方法指导。

Abstract

For easy integration of mechanical transmission and servo control, the ball screw feed system is simplified as a simple mechanical model in the previous research. However, this model is bad for the precise calculation of dynamic performance. Aiming at this problem, taking full consideration of the structure flexibility and internal coupling characteristics of screw-nut, the ball screw feed system multi flexible body dynamics model is built. On this basis, effectively simplified dynamic information of the feed system is extracted accurately with the modal synthesis method and dynamic condensation method in order to accelerate model reduction convergence and cohesion degree response calculation. And the state-space reduction model of ball screw feed system is derived finally. Based on the built-in sensor, dynamic performance test is carried on and this model is validated. The calculation error of first order natural frequency is 5.54%, the experimental and simulation results of the frequency response between torque and rotational are 32.83dB 35.16dB respectively in the first-order natural frequency. This paper provides the important theoretical basis and technical method for the integration modeling of ball screw feed system and servo control system.

关键词

滚珠丝杠进给系统 / 状态空间 / 模态综合 / 动态凝聚

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杨勇1,张为民2，仇炜谏1，陈盛3. 基于模态综合法与动态凝聚的滚珠丝杠进给系统状态空间建模与实验验证[J]. 振动与冲击, 2017, 36(13): 53-59

YANG Yong1,ZHANG Wei-Min2，CHOU Weijian1,CHEN Sheng3. Establishment and experimental verification of ball screw feed system state space modeling based on modal synthesis and dynamic condensation method[J]. Journal of Vibration and Shock, 2017, 36(13): 53-59

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