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

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

马佳^{*, †},
揭豪^*,
白梦昊^*,
彭静^*,
陈辉^*,
陈得良^*, ,

*.
长沙理工大学土木工程学院, 长沙 410114
†.
德国萨尔大学材料科学与工程学院, 萨尔布吕肯 66123

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
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- 文章访问数: 79
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- 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

RESEARCH ON NORMAL RESTITUTION COEFFICIENT BASED ON DIMENSIONLESS ANALYSES

Ma Jia^{*, †},
Jie Hao^*,
Bai Menghao^*,
Peng Jing^*,
Chen Hui^*,
Chen Deliang^{*
, ,}

*.
School of Civil Engineering, Changsha University of Science and Technology, Changsha 410114, China
†.
Department of Material Science and Engineering, Saarland University, Saarbrücken 66123, Germany

摘要

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^*/ρv_nc²与σ_y/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.
- 接触碰撞 /
- 能量耗散 /
- 恢复系数 /
- 无量纲分析 /
- 有限元
Abstract: As an important indicator for the quantification of energy dissipation during the contact/impact process, in-depth researches of the restitution coefficient are of great significance not only for the prediction performance improvement of the existing contact force models, but also for the accurate quantification of contact/impact responses, and the further exploration towards the influence laws of the contact phenomena on the overall system dynamical characteristics. Due to the limitations of current researches, a new restitution coefficient model considering the material properties and initial contact velocities is proposed based on the dimensionless analyses in this work. The specific implementation process can be summarized as follows: Firstly, the contact/impact FEM simulation model between the elastic sphere and the elastic-perfectly plastic substrate is established by using the commercial software ABAQUS, of which the effectiveness can be verified from the setting of minimum mesh sizes of the contact domain and the changing curves of all types of energies during one contact/impact process. Then, large numbers of simulation examples under different working conditions are conducted, and the effects of material property and initial contacting velocity on the contact/impact responses can be thus analyzed. After that, two dimensionless variables, E^*/ρv_nc² and σ_y/E^*, are introduced and the mapping relationships among the restitution coefficient, material properties, and initial contact velocities are explored. In addition, combined with the Johnson theory, the mapping relationship between the yield velocity and material properties is reversely calculated, and thus the novel restitution coefficient model based on the dimensional analyses can be finally established. Comparisons with the experimental data under low contacting velocities and FEM results for high contacting velocities validate the effectiveness and generalization abilities of the presented restitution coefficient model.
- contact/impact process /
- energy loss /
- restitution coefficient /
- dimensionless analyses /
- FEM

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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

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图 2 不同网格尺寸下接触碰撞结果

Figure 2. Simulation results under different mesh sizes

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图 3 接触碰撞力与压入量关系曲线

Figure 3. Contact force vs indentation

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图 4 不同时刻下仿真结果对比

Figure 4. Result comparisons at different stages

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图 5 接触碰撞过程能量变化

Figure 5. Energy changes during the whole process

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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

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图 7 式 (9) 的拟合误差检验

Figure 7. Fitting error of Eq. (9)

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图 8 参数a与k₂间的函数关系

Figure 8. Relation between the parameter a and k₂

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图 9 ρv_y²与σ_y间的关系曲线

Figure 9. Relation between ρv_y² and σ_y

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图 10 参数b与折合弹性模量E*关系

Figure 10. Relation between the parameter b and E*

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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

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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

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图 13 恢复系数模型泛化性能检验

Figure 13. Generalization ability of Eq. (19)

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表 1 材料参数

Table 1. Material parameters

Body	ρ/(kg·m⁻³)	E/GPa	u	σ_y/MPa
Sphere	7850	210	0.3	/
Substrate	7850	210	0.3	500

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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.	Sphere	Substrate	Case No.	Sphere	Substrate	Case No.	Sphere	Substrate
Case No.	ρ/(kg·m^-3)	σ_y/MPa	Case No.	ρ/(kg·m^-3)	σ_y/MPa	Case No.	ρ/(kg·m^-3)	σ_y/MPa
1	3925	300	6	7850	300	11	15700	300
2		500	7		500	12		500
3		700	8		700	13		700
4		1000	9		1000	14		1000
5		1300	10		1300	15		1300

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表 3 试验材料属性

Table 3. Material properties of experiments

Body	Materials	E/GPa	u	σ_y/GPa	ρ/(kg·m⁻³)
sphere	aluminum oxide	370^a	0.22^a	/	3958.226^b
substrate	aluminum	68^a	0.33^a	0.38^a	/
substrate	steel	200^a	0.29^a	1.03^a	/
Notes: ^a From Ref. [22]; ^b From Matweb.com

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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

	Body	E/GPa	u	ρ/(kg·m^-3)	σ_y/MPa
Case 1	sphere	200	0.2	15000	/
Case 1	substrate	70	0.2	7850	200
Case 2	sphere	70	0.3	7000	/
Case 2	substrate	150	0.3	7850	300
Case 3	sphere	150	0.4	7000	/
Case 3	substrate	200	0.4	7850	300
Case 4	sphere	150	0.4	2700	/
Case 4	substrate	200	0.4	7850	300

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