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  

State space modeling and test verification for a ball screw feed system based on modal synthesis and dynamic condensation

作　　者：杨勇[1] 张为民[2] 仇炜谏 陈盛[3] 

机构地区：[1]江苏科技大学机械工程学院,江苏镇江212003 [2]同济大学机械与能源工程学院,上海201804 [3]南京邮电大学自动化学院,南京210023

出　　处：《振动与冲击》2017年第13期53-59,共7页Journal of Vibration and Shock

基　　金：高档数控机床与基础制造装备科技重大专项(2011ZX04016-021);国家科技支撑计划课题(2015BAF06B02-4);江苏省高校自然科学研究面上资助项目(16KJB460017)

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,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32.83 d B和35.16 d B。该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。In order to integrated modeling mechanical transmission segment and servo control system, a ball screw feed system is simplified as a simple mechanical model in previous studies. However, this model is not good for precisely solving its dynamic performance. Here, aiming at this problem, fully considering the structural flexibility and coupling characteristics of screw-nut pair, a ball screw feed system was modeled as a multi-flexible body dynamic model. Then, the dynamic information of the effectively simplified feed system was extracted correctely with the modal synthesis method and dynamic condensation one to speed up the model order reduction and convergence, and condensed DOFs’ responses solving. The state-space reduction model of the ball screw feed system was derived finally. Based on the built-in sensors, the system, s dynamic performance tests were conducted to verify the correctness of this model. It was shown that the calculation error of the model,s the first order natural frequency is 5. 54% , the test and simulation results of the system,s frequency responses are 32. 83 dB and 35. 16 dB at the first-order natural frequency point, respectively. The study results provided an important theoretical basis and a technical guide for integrated modeling a ball screw feed system and its 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 

分 类 号：TH132.1[机械工程—机械制造及自动化]