A novel nonlinear contact stiffness model of concrete–steel joint based on the fractal contact theory
A novel nonlinear contact stiffness model of concrete–steel joint based on the fractal contact theory
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DOI：
10.1007/s11071-018-4350-7
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发表时间：
2018-05
影响因子：
5.6
通讯作者：
Yongsheng Zhao;Hongchao Wu;Zhifeng Liu;Qiang Cheng;Cong-bin Yang
中科院分区：
文献类型：
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作者：
Yongsheng Zhao;Hongchao Wu;Zhifeng Liu;Qiang Cheng;Cong-bin Yang
重型机床通常安装在混凝土基础中，机床与基础的连接对机床的工作精度和使用寿命有着至关重要的影响。基于分形理论，提出了一种新的钢筋混凝土节点接触刚度模型。钢-混凝土节点接触面形貌具有分形特征，可用分形参数描述。微凸体在微观尺度上被视为弹性、塑性变形。但当应力超过其屈服极限时，混凝土表面的微凸体将被压碎。然后，接触表面的力平衡将被打破。本文提出了一种描述钢-混凝土节点接触状态的迭代模型。由于接触微凸体所占的比例很小（小于1%），因此破碎微凸体上的载荷被假定为由其他非接触微凸体承载。这个过程将一次又一次地重复，直到在外部载荷下不产生压碎的粗糙体。在此基础上，通过对接触面粗糙度的积分，计算出节点的真实的接触面积、接触刚度。该模型可以揭示接触刚度与载荷、分形粗糙度参数G、分形维数D之间的非线性关系。设计了一个混凝土-钢试件的实验装置来验证所提出的模型。结果表明，理论振型与实验变化振型吻合较好。理论固有频率与实验固有频率的误差小于4.18%。该模型可用于预测钢-混凝土节点的接触刚度，为机床-混凝土基础的连接特性优化提供理论依据。
The heavy-duty machine tool is usually assumed in the concrete foundation, in which the machine tool-foundation joints have a critical effect on the working accuracy and life of heavy-duty machine tool. This paper proposed a novel contact stiffness model of concrete–steel joint based on the fractal theory. The topography of contact surface exist in concrete–steel joint has a fractal feature and can be described by fractal parameters. Asperities are considered as elastic, plastic deformation in micro-scale. However, the asperities of concrete surface will be crushed when the stress is larger than their yield limit. Then, the force balance of contact surfaces will be broken. Here, an iteration model is proposed to describe the contact state of concrete–steel joint. Because the contact asperities cover a very small proportion (less than 1%), the load on crushed asperities is assumed carried by other no contact asperities. This process will be repeated again and again until the crushed asperities are not being produced under external load. After that, the real contact area, contact stiffness of the concrete–steel joint can be calculated by integrating the asperities of contact surfaces. Nonlinear relationships between contact stiffness and load, fractal roughness parameterG, fractal dimensionDcan be revealed based on the presented model. An experimental setup with concrete–steel test-specimens is designed to validate the proposed model. Results indicate that the theoretical vibration mode shapes agree well with the experimental variation mode shapes. The errors between theoretical and experimental natural frequencies are less than 4.18%. The presented model can be used to predict the contact stiffness of concrete–steel joint, which will provide a theoretical basis for optimizing the connection characteristic of machine tool-concrete foundation.