EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于无量纲分析的法向恢复系数模型研究

马佳 揭豪 白梦昊 彭静 陈辉 陈得良

马佳, 揭豪, 白梦昊, 彭静, 陈辉, 陈得良. 基于无量纲分析的法向恢复系数模型研究. 力学学报, 2023, 55(4): 1-9 doi: 10.6052/0459-1879-22-583
引用本文: 马佳, 揭豪, 白梦昊, 彭静, 陈辉, 陈得良. 基于无量纲分析的法向恢复系数模型研究. 力学学报, 2023, 55(4): 1-9 doi: 10.6052/0459-1879-22-583
Ma Jia, Jie Hao, Bai Menghao, Peng Jing, Chen Hui, Chen Deliang. Research on normal restitution coefficient based on dimensionless analyses. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(4): 1-9 doi: 10.6052/0459-1879-22-583
Citation: Ma Jia, Jie Hao, Bai Menghao, Peng Jing, Chen Hui, Chen Deliang. Research on normal restitution coefficient based on dimensionless analyses. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(4): 1-9 doi: 10.6052/0459-1879-22-583

基于无量纲分析的法向恢复系数模型研究

doi: 10.6052/0459-1879-22-583
基金项目: 国家自然科学基金(12002065), 湖南省自然科学基金(2021JJ40556), 国家留学基金委博士后项目(202008430121)资助
详细信息
    通讯作者:

    陈得良, 教授, 主要研究方向为动力学与控制. E-mail: deliang_chen@126.com

  • 中图分类号: O3

RESEARCH ON NORMAL RESTITUTION COEFFICIENT BASED ON DIMENSIONLESS ANALYSES

  • 摘要: 作为描述接触碰撞过程能量损失的重要参量, 恢复系数的深入研究对于提升现有接触碰撞力模型预测性能、准确描述接触碰撞现象, 并进一步探明其对机械系统整体动态特性影响规律方面具有重要作用. 鉴于现有恢复系数模型计算精度的局限性, 本文基于无量纲分析方法, 提出了一种考虑材料特性与初始碰撞速度的新型恢复系数模型. 具体实施过程如下: 首先, 利用有限元软件ABAQUS建立弹性球−理想弹塑性基底法向接触碰撞数值仿真模型, 分别从最小网格尺寸设置与接触碰撞能量转换角度验证了所建模型的有效性; 基于此模型开展多工况下的数值模拟研究, 分析不同材料弹塑性参数与初始碰撞速度对接触碰撞响应的影响; 在此基础上, 引入无量纲化参数E*/ρvnc2σy/E*, 寻找恢复系数与弹塑性参数及初始碰撞速度间的函数关系; 进一步结合Johnson塑性碰撞理论, 反向推算获取屈服速度与材料属性的映射关系, 最终建立无量纲化恢复系数新模型; 通过与低速试验数据、高速有限元模拟结果的对比, 验证了新模型的预测精度和泛化性能.

     

  • 图  1  小球与基底正碰撞数值仿真模型

    Figure  1.  Normal contact FEM model between the sphere and substrate

    图  2  不同网格尺寸下接触碰撞结果

    Figure  2.  Simulation results under different mesh sizes

    图  3  接触碰撞力与压入量关系曲线

    Figure  3.  Contact force vs indentation

    图  4  不同时刻下仿真结果对比

    Figure  4.  Result comparisons at different stages

    图  5  接触碰撞过程能量变化

    Figure  5.  Energy changes during the whole process

    图  6  恢复系数与无量纲化参量k1关系曲线

    Figure  6.  Relations between restitution coefficient and k1

    图  7  式 (9) 的拟合误差检验

    Figure  7.  Fitting error of Eq. (9)

    图  8  参数ak2间的函数关系

    Figure  8.  Relation between the parameter a and k2

    图  9  ρvy2σy间的关系曲线

    Figure  9.  Relation between ρvy2 and σy

    图  10  参数b与折合弹性模量E*关系

    Figure  10.  Relation between the parameter b and E*

    图  11  氧化铝小球与铝材基底接触碰撞过程恢复系数结果对比

    Figure  11.  Comparisons of the restitution coefficient between the alumina sphere and aluminum substrate

    图  12  氧化铝小球与钢材基底接触碰撞过程恢复系数结果对比

    Figure  12.  Comparisons of the restitution coefficient between the alumina sphere and steel substrate

    图  13  恢复系数模型泛化性能检验

    Figure  13.  Generalization ability of Eq. (19)

    表  1  材料参数

    Table  1.   Material parameters

    Bodyρ/(kg·m−3)E/GPauσy/MPa
    Sphere78502100.3/
    Substrate78502100.3500
    下载: 导出CSV

    表  2  恢复系数模型仿真参数

    Table  2.   Simulation parameters for the establishment of the restitution coefficient model

    Case No.SphereSubstrateCase No.SphereSubstrateCase No.SphereSubstrate
    ρ/(kg·m-3)σy/MPaρ/(kg·m-3)σy/MPaρ/(kg·m-3)σy/MPa
    13925300678503001115700300
    2500750012500
    3700870013700
    4100091000141000
    51300101300151300
    下载: 导出CSV

    表  3  试验材料属性

    Table  3.   Material properties of experiments

    BodyMaterialsE/GPauσy/GPaρ/(kg·m−3)
    spherealuminum oxide370a0.22a/3958.226b
    substratealuminum68a0.33a0.38a/
    steel200a0.29a1.03a/
    Notes: a From Ref. [22]; b From Matweb.com
    下载: 导出CSV

    表  4  泛化性能验证材料参数

    Table  4.   Material parameters for the verification of the generalization ability of the new model

    BodyE/GPauρ/(kg·m-3)σy/MPa
    Case 1sphere2000.215000/
    substrate700.27850200
    Case 2sphere700.37000/
    substrate1500.37850300
    Case 3sphere1500.47000/
    substrate2000.47850300
    Case 4sphere1500.42700/
    substrate2000.47850300
    下载: 导出CSV
  • [1] 曹登庆, 白坤朝, 丁虎等. 大型柔性航天器动力学与振动控制研究进展. 力学学报, 2019, 51(1): 1-13 (Cao Dengqing, Bai Kunchao, Ding Hu, et al. Advances in dynamics and vibration control of large-scale flexible spacecraft. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 1-13 (in Chinese) doi: 10.6052/0459-1879-18-054
    [2] 王乙坤, 王琳, 倪樵等. 具有刚性间隙约束输流管的碰撞振动. 力学学报, 2020, 52(5): 1498-1508 (Wang Yikun, Wang Lin, Ni Qiao, et al. Vibro-impact dynamics of pipe conveying fluid subjected to rigid clearance constraint. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1498-1508 (in Chinese) doi: 10.6052/0459-1879-20-137
    [3] 宁志远, 白争锋, 蒋鑫等. 磨损与动力学耦合的行星传动齿轮动力学研究. 力学学报, 2022, 54(4): 1125-1135 (Ning Zhiyuan, Bai Zhengfeng, Jiang Xin, et al. Study on dynamics of planetary transmission gear considering wear and dynamics coupling. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(4): 1125-1135 (in Chinese) doi: 10.6052/0459-1879-21-554
    [4] Hertz H. Über die berührung fester elastische körper. Journal für die reine und Angewandte Mathematik, 1882, 92: 156-171
    [5] Zhang J, Liang X, Zhang ZH, et al. A continuous contact force model for impact analysis. Mechanical Systems and Signal Processing, 2022, 168: 108739 doi: 10.1016/j.ymssp.2021.108739
    [6] 郭祥, 靳艳飞, 田强. 随机空间柔性多体系统动力学分析. 力学学报, 2020, 52(6): 1730-1742 (Guo Xiang, Jin Yanfei, Tian Qiang. Dynamics analysis of stochastic spatial flexible multibody system. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1730-1742 (in Chinese) doi: 10.6052/0459-1879-20-273
    [7] Wang H, Yin XC, Deng QM, et al. Experimental and theoretical analyses of elastic-plastic repeated impacts by considering wave effects. European Journal of Mechanics-A/Solids, 2017, 65: 212-222 doi: 10.1016/j.euromechsol.2017.04.006
    [8] Hunt KH, Crossley FRE. Coefficient of restitution interpreted as damping in vibroimpact. Journal of Applied Mechanics, 1975, 42(2): 1-6
    [9] Lankarani HM, Nikravesh PE. Continuous contact force models for impact analysis in multibody systems. Nonlinear Dynamics, 1994, 5(2): 193-207 doi: 10.1007/BF00045676
    [10] Flores P, Machado M, Silva MT, et al. On the continuous contact force models for soft materials in multibody dynamics. Multibody System Dynamics, 2011, 25(3): 357-375 doi: 10.1007/s11044-010-9237-4
    [11] 王旭鹏, 张艳, 吉晓民等. 一种基于变恢复系数的接触碰撞力模型. 振动与冲击, 2019, 38(5): 198-202 (Wang Xupeng, Zhang Yan, Ji Xiaomin, et al. A contact-impact force model based on variable recovery coefficient. Journal of Vibration and Shock, 2019, 38(5): 198-202 (in Chinese) doi: 10.13465/j.cnki.jvs.2019.05.028
    [12] 姚文莉, 岳嵘. 有争议的碰撞恢复系数研究进展. 振动与冲击, 2015, 34(19): 43-48 (Yao Wenli, Yue Rong. Advance in controversial restitution coefficient study for impact problems. Journal of Vibration and Shock, 2015, 34(19): 43-48 (in Chinese) doi: 10.13465/j.cnki.jvs.2015.19.007
    [13] 王庚祥, 马道林, 刘洋等. 多体系统碰撞动力学中接触力模型的研究进展. 力学学报, 2022, 54(11): 1-28 (Wang Gengxiang, Ma Daolin, Liu Yang, et al. Research progress of contact force models in the collision mechanics of multibody system. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(11): 1-28 (in Chinese)
    [14] 骞朋波, 尹晓春, 沈煜年等. 碰撞激发弹塑性波传播的动态子结构方法. 力学学报, 2012, 44(1): 184-188 (Qian Pengbo, Yin Xiaochun, Shen Yunian, et al. Dynamic substructure method for elastic-plastic wave propagation induced by impact. Journal of Applied Mechanics, 2012, 44(1): 184-188 (in Chinese) doi: 10.6052/0459-1879-2012-1-lxxb2011-186
    [15] Patil D, Higgs CF. A coefficient of restitution model for sphere–plate elastoplastic impact with flexural vibrations. Nonlinear Dynamics, 2017, 88(3): 1817-1832 doi: 10.1007/s11071-017-3346-z
    [16] Wu CY. Finite element analysis of particle impact problems [PhD Thesis], U K: The University of Aston in Birmingham, 2001
    [17] Hutchings IM. Energy absorbed by elastic waves during plastic impact. Journal of Physics D:Applied Physics, 1979, 12(11): 1819-1824 doi: 10.1088/0022-3727/12/11/010
    [18] Johnson KL. Contact Mechanics. Cambridge: Cambridge University Press; 1985
    [19] Thornton C. Coefficient of restitution for collinear collisions of elastic-perfectly plastic spheres. Journal of Applied Mechanics, 1997, 64: 383-386 doi: 10.1115/1.2787319
    [20] Wu CY, Li LY, Thornton C. Rebound behaviour of spheres for plastic impacts. International Journal of Impact Engineering, 2003, 28(9): 929-946 doi: 10.1016/S0734-743X(03)00014-9
    [21] 葛藤, 贾智宏, 周克栋. 钢球和刚性平面弹塑性正碰撞恢复系数研究. 工程力学, 2008(6): 209-213 (Ge Teng, Jia Zhihong, Zhou Kedong. Research on elastoplastic normal impact of steel. Engineering Mechanics, 2008(6): 209-213 (in Chinese)
    [22] Jackson RL, Green I, Marghitu DB. Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres. Nonlinear Dynamics, 2010, 60(3): 217-229 doi: 10.1007/s11071-009-9591-z
    [23] Etsion I, Kligerman Y, Kadin Y. Unloading of an elastic-plastic loaded spherical contact. International Journal of Solids and Structures, 2005, 42(13): 3716-3729 doi: 10.1016/j.ijsolstr.2004.12.006
    [24] Jackson RL, Green I. A finite element study of elasto-plastic hemispherical contact against a rigid flat. Journal of Tribology, 2005, 127(2): 343-354 doi: 10.1115/1.1866166
    [25] 郭振, 陈渭, 耿煜等. 恒定外力作用下的碰撞过程恢复系数模型研究. 振动与冲击, 2021, 40(12): 62-69 (Guo Zhen, Chen Wei, Geng Yu, et al. A study on the coefficient of a restitution model considering constant external forces during impact. Journal of Vibration and Shock, 2021, 40(12): 62-69 (in Chinese) doi: 10.13465/j.cnki.jvs.2021.12.009
    [26] 袁晗, 王小军, 张宏剑等. 重复使用火箭着陆结构稳定性分析. 力学学报, 2020, 52(4): 1007-1023 (Yuan Han, Wang Xiaojun, Zhang Hongjian, et al. Stability analysis of reusable launch vehicle landing structure. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 1007-1023 (in Chinese) doi: 10.6052/0459-1879-20-069
    [27] 马佳, 董帅, 唐雪松等. 以提升创新能力为目标的基础力学实践教学初探. 力学与实践, 2022, 44(3): 706-711 (Ma Jia, Dong Shuai, Tang Xuesong, et al. Preliminary research of practice teaching for fundamental mechanics targeted at the improvement of innovation ability. Mechanics in Engineering, 2022, 44(3): 706-711 (in Chinese) doi: 10.6052/1000-0879-21-479
    [28] 彭光健, 张泰华. 表面残余应力的仪器化压入检测方法研究进展. 力学学报, 2022, 54(8): 2287-2303 (Peng Guangjian, Zhang Taihua. Progress in instrumented indentation methods for determination of surface residual stress. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(8): 2287-2303 (in Chinese) doi: 10.6052/0459-1879-22-222
    [29] 宋明泽. 金属铍纳米压入行为(性能)[硕士论文]. 宁夏: 宁夏大学, 2022

    Song Mingze. Nanoidentation behaviors (properties) of metal beryllium [Master's Thesis]. Ningxia: Ningxia University, 2022(in Chinese))
    [30] Ma DL, Liu CS. Contact law and coefficient of restitution in elastoplastic spheres. Journal of Applied Mechanics, 2015, 82(12): 121006 doi: 10.1115/1.4031483
    [31] Chang WR, Ling FF. Normal impact model of rough surfaces. Journal of Tribology, 1992, 114(3): 439-447 doi: 10.1115/1.2920903
    [32] Weir G, Tallon S. The coefficient of restitution for normal incident, low velocity particle impacts. Chemical Engineering Science, 2005, 60(13): 3637-3647 doi: 10.1016/j.ces.2005.01.040
    [33] 蒋志明, 刘强, 陈人河等. 安庆铜矿主溜井非贮矿段矿石流冲击磨损规律相似模型试验. 长沙理工大学学报(自然科学版), 2020, 17(3): 22-29

    Jiang Zhiming, Liu Qiang, Chen Renhe, et al. Similar model test on flow impact wear law in the non-storage section of main ore-pass in Anqing copper mine. Journal of Changsha University of Science and Technology (Natural Science). 2020, 17(3): 22-29(in Chinese))
    [34] Peng Q, Jin Y, Liu X, et al. Effect of plasticity on the coefficient of restitution of an elastoplastic sphere impacting an elastic plate. International Journal of Solids and Structures, 2021, 222-223: 111036 doi: 10.1016/j.ijsolstr.2021.03.023
    [35] Kharaz AH, Gorham DA. A study of the restitution coefficient in elastic-plastic impact. Philosophical Magazine Letters, 2000, 80(8): 549-559 doi: 10.1080/09500830050110486
  • 加载中
图(13) / 表(4)
计量
  • 文章访问数:  79
  • HTML全文浏览量:  18
  • PDF下载量:  22
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-10-20
  • 录用日期:  2022-12-29
  • 网络出版日期:  2022-12-30

目录

    /

    返回文章
    返回