RESEARCH ON NORMAL RESTITUTION COEFFICIENT BASED ON DIMENSIONLESS ANALYSES
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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*/ρvnc2与σy/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.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*/ρvnc2 and σy/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.
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Key words:
- contact/impact process /
- energy loss /
- restitution coefficient /
- dimensionless analyses /
- FEM
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表 1 材料参数
Table 1. Material parameters
Body ρ/(kg·m−3) E/GPa u σy/MPa Sphere 7850 210 0.3 / Substrate 7850 210 0.3 500 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 ρ/(kg·m-3) σy/MPa ρ/(kg·m-3) σy/MPa ρ/(kg·m-3) σy/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 表 3 试验材料属性
Table 3. Material properties of experiments
Body Materials E/GPa u σy/GPa ρ/(kg·m−3) sphere aluminum oxide 370a 0.22a / 3958.226b substrate aluminum 68a 0.33a 0.38a / steel 200a 0.29a 1.03a / Notes: a From Ref. [22]; b From Matweb.com 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) σy/MPa Case 1 sphere 200 0.2 15000 / substrate 70 0.2 7850 200 Case 2 sphere 70 0.3 7000 / substrate 150 0.3 7850 300 Case 3 sphere 150 0.4 7000 / substrate 200 0.4 7850 300 Case 4 sphere 150 0.4 2700 / substrate 200 0.4 7850 300 -
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