滚珠丝杠传动系统线性变参数动力学模型试验建模方法

doi:10.3901/JME.2022.09.098

机械工程学报 ›› 2022, Vol. 58 ›› Issue (9): 98-106.doi: 10.3901/JME.2022.09.098

扫码分享

滚珠丝杠传动系统线性变参数动力学模型试验建模方法

黄涛^1,2, 杜双江^1,2, 张钎^1,2, 曹华军^1,2

1. 重庆大学机械与运载工程学院重庆 400044;
2. 重庆大学机械传动国家重点实验室重庆 400044

收稿日期:2021-05-18 修回日期:2022-01-08 出版日期:2022-05-05 发布日期:2022-06-23
通讯作者: 曹华军(通信作者)，男，1978年出生，博士，教授，博士研究生导师。主要研究方向为绿色低碳制造基础理论，高速干切工艺及智能装备，高性能传动系统。E-mail：hjcao@cqu.edu.cn E-mail:hjcao@cqu.edu.cn
作者简介:黄涛，男，1986年出生，博士，副教授，博士研究生导师。主要研究方向为精密/超精密传动系统动力学与控制。E-mail：thuang@cqu.edu.cn
基金资助:
国家重点研发计划(2018YFB1701203)、国家自然科学基金(51805053)和中央高校基本科研业务费专项资金(2020CDJGFJX010)资助项目

Experimental Modeling of Linear Parameter Varying Dynamics Model of Ball Screw Drive System

HUANG Tao^1,2, DU Shuangjiang^1,2, ZHANG Qian^1,2, CAO Huajun^1,2

1. College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing 400044;
2. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044

Received:2021-05-18 Revised:2022-01-08 Online:2022-05-05 Published:2022-06-23

摘要/Abstract

摘要： 准确建立滚珠丝杠传动系统动力学模型是实现高速、高加速度和高精度运动控制的基础。滚珠丝杠传动系统的动力学特性具有不确定性，实际是随位置、负载质量等变量变化的，数学上应描述为变参数模型。因此，一种滚珠丝杠传动系统线性变参数(Linear parameter varying, LPV)动力学模型实验建模方法被提出。通过局部频域辨识方法获得非参数模型，并采用非线性最小二乘方法得到模态叠加形式的传递函数模型。采用傅里叶级数形式的正交基函数拟合方法，对不同位置下的局部传递函数模型参数进行拟合，获得与位置相关的参数模型。基于拟合结果，选择合适的工况点进行三次样条插值，得到与位置、负载质量相关的LPV模型。所提出方法应用于滚珠丝杠试验台，获得了一个与全局位置、负载质量相关性高的LPV模型，为实现基于LPV模型的高速、高精度运动控制提供了基础。

关键词: 滚珠丝杠, 线性变参数, 系统辨识, 参数拟合, 插值

Abstract: Accurate modeling of the dynamics of ball screw drive system is the foundation for high speed, high acceleration and high precision motion control. The dynamics of the ball screw drive system has uncertainties and actually changes with position, load and other variables, which should be described as a variable parameter model in mathematics. Therefore, an experimental modeling method of linear parameter varying (LPV) dynamic model of ball screw drive system is proposed. Specially, the nonparametric model is obtained by the local frequency domain identification method, and the transfer function model in the form of modal superposition is obtained by the nonlinear least squares method. Then, an orthogonal basis function fitting method in the form of Fourier series is utilized to fit the local transfer function model parameters at different positions to obtain the position-dependent parameter model. Based on the fitting results, the position- and load-dependent LPV model is obtained by selecting suitable working points for third spline interpolation. The proposed method is applied to a developed ball screw experimental system to obtain a LPV model with high correlation to the full working position and load, which provides a basis for realizing high-speed and high-precision motion control based on the LPV model.

Key words: ball screw, linear parameter varying, system identification, parameter fitting, interpolation

中图分类号:

TH113
N945

黄涛, 杜双江, 张钎, 曹华军. 滚珠丝杠传动系统线性变参数动力学模型试验建模方法[J]. 机械工程学报, 2022, 58(9): 98-106.

HUANG Tao, DU Shuangjiang, ZHANG Qian, CAO Huajun. Experimental Modeling of Linear Parameter Varying Dynamics Model of Ball Screw Drive System[J]. Journal of Mechanical Engineering, 2022, 58(9): 98-106.

参考文献

[1] LI Jie, XIE Fugui, LIU Xinjun, et al. Dynamic analysis of linear feed system under the action of electromechanical rigid flexible coupling characteristics[J]. Journal of Mechanical Engineering, 2017, 53(17): 60-69. 李杰, 谢福贵, 刘辛军, 等. 机电-刚柔耦合特性作用下线性进给系统动力学分析[J]. 机械工程学报, 2017, 53(17): 60-69.
[2] ALTINTAS Y, VERL A, BRECHER C, et al. Machine tool feed drives[J]. CIRP Annals, 2011, 60(2): 779-796.
[3] KIM D, AHN J, CAMPBELL O, et al. Investigations of a robotic test bed with viscoelastic liquid cooled actuators[J]. IEEE/ASME Transactions on Mechatronics, 2018, 23(6): 2704-2714.
[4] DUMANLI A, SENCER B. Optimal high-bandwidth control of ball-screw drives with acceleration and jerk feedback[J]. Precision Engineering, 2018, 54: 254-268.
[5] VARANASI K K, NAYFEH S A. The dynamics of lead-screw drives: low-order modeling and experiments[J]. Journal of Dynamic Systems, Measurement, and Control, 2004, 126(2): 388-396.
[6] DADALAU A, MOTTAHEDI M, GROH K, et al. Parametric modeling of ball screw spindles[J]. Production Engineering, 2010, 4(6): 625-631
[7] OKWUDIRE C. Finite element modeling of ballscrew feed drive systems for control purposes[D]. Vancouver: University of British Columbia, 2005.
[8] DONG Liang, TANG Wencheng. Hybrid modeling and analysis of structural dynamic of a ball screw feed drive system[J]. Mechanics, 2013, 19(3): 316-323.
[9] WANG Nan, LIN Weiyang. Robust tracking control of AC servo system including a ball screw[J]. Neurocomputing, 2016, 179: 110-117.
[10] HENKE B, SAWODNY O, NEUMANN R. Distributed parameter modeling of flexible ball screw drives using ritz series discretization[J]. IEEE/ASME Transactions on Mechatronics, 2014, 20(3): 1226-1235.
[11] QIAN Rongrong, LUO Minzhou, ZHAO Jianghai, et al. Modeling and vibration research of ball screw drive system based on Ritz series[J]. Journal of System Simulation, 2017, 29(10): 2268. 钱荣荣, 骆敏舟, 赵江海, 等. 基于Ritz级数的滚珠丝杠驱动系统建模与振动研究[J]. 系统仿真学报, 2017, 29(10): 2268.
[12] ANSOATEGUI I, CAMPA F J. Mechatronics of a ball screw drive using an N degrees of freedom dynamic model[J]. The International Journal of Advanced Manufacturing Technology, 2017, 93(1): 1307-1318.
[13] VICENTE D A, HECKER R L, VILLEGAS F J, et al. Modeling and vibration mode analysis of a ball screw drive[J]. The International Journal of Advanced Manufacturing Technology, 2012, 58(1): 257-265.
[14] ZHANG Huijie, LIU Hui, DU Chao, et al. Dynamics analysis of a slender ball-screw feed system considering the changes of the worktable position[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2019, 233(8): 2685-2695.
[15] ZHAO Jiajia, LIN Mingxing, SONG Xianchun, et al. Modeling and analysis of full ball load distribution of ball screw pair under compound load [J]. Journal of Mechanical Engineering, 2020, 56(17): 126-136. 赵佳佳, 林明星, 宋现春, 等. 复合载荷下滚珠丝杠副全滚珠载荷分布建模与分析[J]. 机械工程学报, 2020, 56(17): 126-136.
[16] NAGAMUNE R, CHOI J. Parameter reduction in estimated model sets for robust control[J]. Journal of Dynamic Systems, Measurement, and Control, 2010, 132(2): 218-229.
[17] MCKELVEY T. Frequency domain identification[J]. IFAC Proceedings Volumes, 2000, 33(15): 7-18.
[18] PINTELON R, SCHOUKENS J. System identification: A frequency domain approach[M]. New York: John Wiley & Sons, 2012.
[19] RANGANATHAN A. The levenberg-marquardt algorithm[J]. Tutoral on LM Algorithm, 2004, 11(1): 101-110.
[20] VAN DEN HOF P, NINNESS B. System identification with generalized orthonormal basis functions[C]// Modelling and Identification with Rational Orthogonal Basis Functions. Springer, London, 2005: 61-102.
[21] HAREL O. The estimation of R 2 and adjusted R 2 in incomplete data sets using multiple imputation[J]. Journal of Applied Statistics, 2009, 36(10): 1109-1118.
[22] SZÉKELY G J, RIZZO M L, BAKIROV N K. Measuring and testing dependence by correlation of distances[J]. The Annals of Statistics, 2007, 35(6): 2769-2794.

滚珠丝杠传动系统线性变参数动力学模型试验建模方法

Experimental Modeling of Linear Parameter Varying Dynamics Model of Ball Screw Drive System

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	李玲, 云强强, 王晶晶, 东亚斌, 史小辉. 具有连续光滑特性的结合面接触刚度模型[J]. 机械工程学报, 2021, 57(7): 117-124.
[2]	陈道云, 肖乾, 孙守光, 牟明慧. 强耦合结构动载荷识别方法[J]. 机械工程学报, 2021, 57(4): 174-181.
[3]	朱本亮, 张宪民, 李海, 王日鑫, 刘敏, 李昊. 基于节点密度插值的多材料柔顺机构拓扑优化[J]. 机械工程学报, 2021, 57(15): 53-61.
[4]	朱何荣,方佳维,陈桂友,王敏,熊慕文. 智能变电站同步系统对测量设备的影响及其处理策略[J]. 电气工程学报, 2020, 15(3): 143-149.
[5]	赵佳佳, 林明星, 宋现春, 骆伟超, 宋丽伟. 复合载荷下滚珠丝杠副全滚珠载荷分布建模与分析[J]. 机械工程学报, 2020, 56(17): 126-136.
[6]	裴元帅, 王定标, 王晓亮, 王光辉, 袁洪琳. 基于拓扑优化的风冷热沉研究[J]. 机械工程学报, 2020, 56(16): 91-97.
[7]	孙博华, 邓伟文, 吴坚, 李雅欣. 虚拟随机车路场下驾驶人驾驶能力机理分析[J]. 机械工程学报, 2020, 56(16): 166-180.
[8]	孙志毅, 张韵悦, 李虹, 孙前来, 王银. 挖掘机的最优时间轨迹规划[J]. 机械工程学报, 2019, 55(5): 166-174.
[9]	李志农, 李云龙, 刁海洋. 基于非线性输出频率响应函数的转子不对中-碰摩耦合故障诊断方法研究[J]. 机械工程学报, 2019, 55(19): 84-91.
[10]	王灏, 黄家海, 权龙, 王鹤. 基于双线性插值控制策略的比例流量阀特性研究[J]. 机械工程学报, 2018, 54(20): 287-296.
[11]	杜义贤, 李涵钊, 谢黄海, 田启华, 周祥曼, 罗震. 基于序列插值模型和多重网格方法的多材料柔性机构拓扑优化[J]. 机械工程学报, 2018, 54(13): 47-56.
[12]	韩飞燕, 张定华, 吴宝海, 张莹. 基于变形映射的多轴粗加工工序模型建立方法^*[J]. 机械工程学报, 2017, 53(3): 155-161.
[13]	赵帅, 黄亦翔, 王浩任, 刘成良, 刘晓, 梁鑫光. 基于拉普拉斯特征马氏距离的滚珠丝杠健康评估[J]. 机械工程学报, 2017, 53(15): 125-130.
[14]	孙喆, 赵晶晶, 时振刚. 电磁轴承支承柔性转子模型测试与辨识[J]. 机械工程学报, 2016, 52(8): 16-22.
[15]	王恒, 张俊杰, 王永泉, 陈花玲. 考虑反向器影响的滚珠丝杠副摩擦力矩计算模型[J]. 机械工程学报, 2016, 52(7): 97-103.