界面接触非线性振动机理与能量耗散研究
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摘要
机械界面的接触振动特性与能量耗散机理的解明与否，不仅直接影响机械装备的动态服役性能，而且影响监控机器特征振动信号的幅度、频率和相位等信息，是导致设备状态监控的准确性和可靠性低的主要原因。
由于机械接触界面的复杂性和多样性，目前，一些重要的现象和机理尚未解明，尤其是界面的接触刚度和界面阻尼特性、复杂界面特性的界面模型表征、界面的非线性动力学过程、多界面的接触振动现象及其对系统的影响等核心问题一直未得到很好解决。目前，机械界面行为已经成为机械领域中的关键共性的基础科学问题。因此，开展界面接触动力学行为的探索性研究，具有重要的理论意义和实际工程价值。
本论文重点围绕几类基础的接触界面，包括考虑重力作用的球面接触界面、粗糙接触界面、滑移接触界面和层叠多传递界面，通过建立界面接触的动力学模型，研究两类典型界面的接触刚度和阻尼特性，揭示三种典型界面的接触振动与能量耗散特性，以及激励载荷在层叠多界面的振动与能量传递行为，并通过相关实验验证关键模型和计算结果的有效性和准确性。论文的主要工作有以下几个方面：
①针对目前基于Hertz球-刚性平面接触模型，因受接触界面属性、阻尼属性及其他因素的影响，线性粘性阻尼模型难以真实描述界面接触力-变形关系的问题，在考虑真实系统的重力影响因素的基础上，采用任意正指数的非线性粘性阻尼函数，建立了基于静平衡位置的球体-刚性平面接触振动模型，分析了不同的界面非线性阻尼对系统自由振动响应的影响；同时，针对系统响应特征基本相同，通过响应值辨识接触阻尼模型困难的问题，基于接触阻尼回复力-速度关系，提出了一种基于回复力的接触阻尼模型辨识方法，且通过实验方法验证了其有效性，并获得了多种材料属性的球-平面模型的阻尼模型。
②建立了“单层金属板-刚性平面”粗糙界面模型和“多层粗糙金属板-刚性平面”多界面模型，耦合了粗糙表面的分形模型、塑性材料的连续性硬化准则和加载与卸载力-变形曲线形成迟滞环面积等于塑性变形能量耗散量的关系，可较好地解决弹性和塑形的转变过程存在不连续的问题。同时，研究了界面形貌、材料塑性变形行为和界面摩擦对粗糙界面的接触力-变形关系的影响，计算了由塑性变形及硬化引起的能量耗散和多层粗糙界面的能量传递耗散率，揭示了粗糙界面塑性接触变形机理和能量耗散规律。
③采用具有自相似和尺度独立的粗糙表面分形模型，通过计算不同界面形貌接触模型的力-变形关系，构造了粗糙接触界面和表面粗糙体的刚度表达式，建立了基于静平衡位置的弹性粗糙体-刚性平面的粗糙界面接触振动模型，可克服目前粗糙界面的接触刚度、动力学行为和能量耗散基于粗糙表面的统计学模型描述而具有尺度依赖性的缺点。同时，研究了界面形貌对法向接触刚度的影响，计算了不同形貌界面接触振动系统的固有频率和振动能量耗散率，分析了粗糙界面法向接触振动的响应特征与能量耗散特性，并对界面法向微动能量耗散的实验结果进行了解释。
④推导了无滑动、微滑动和整体滑动的不同界面运动状态时滑动界面端部的力-位移关系表达式，建立了滑动界面系统沿滑动方向的动力学模型，解决了目前的滑动界面系统模型局限于界面具有均匀压力分布的假设条件，且仅考虑界面微滑动对系统振动响应特性影响的问题，并在考虑真实界面的非均匀压力分布的基础上，计算了不同滑动界面运动状态滑动界面系统的固有频率、简谐载荷作用下的响应幅值以及每周期的能量损耗量，研究了动态载荷作用下滑动界面系统的动力学响应与能量耗散特性。
⑤考虑实际传递界面法向和切向运动耦合，扩展单一滑动界面模型，建立了“球-螺栓固结多层叠加板”的叠加多传递界面模型（SJAMP），计算了不同冲击激励下多层叠加金属板多传递界面的加速度响应，构造了振动加速度幅值与冲击激励的关系表达式，引入振动传递率与能量传递率的概念并计算了各传递界面的振动与能量传递率，分析了输入界面对冲击能量的传递率与冲击能量的关系，以及冲击激励沿非连续多界面传递时的振动与能量传递特性，并通过实验测试验证了计算结果的可靠性。
The vibration characteristics and energy dissipation mechanism at contactinterfaces not only significantly affect the dynamic performance of mechanical system,but also greatly affect the amplitude, frequency and phase responses of measuredcharacteristic signal, and thus further influence the accuracy and reliability of machinerycondition mointering. Due to the complexity and diversity of contact interfacesassociated with mechanical system, the mechanism of some very importantphenomenons are unclear, especially the critical problems as stiffness and dampingcharacteristics at contact interfaces, model characterization for interface with complexattribution, nonlinear dynamic process, contact vibration at multiple interfaces and itseffect on system. The interface properties have become the basic key problem inmechanical area. Therefore, it is of great significance to explore the contact dynamics atinterfaces.
This thesis foucuses on the nonlinear vibration characteristics and energydissipation mechanism of several basic contact interfaces, including sphere contactinterface considered the effect of gravity, rough contact interface, sliding contactinterface and layered multiple transmitting interfaces. The dynamic models areestablished and the contact stiffness and damping characteristics of two type interfaces,i.e., the sphere and the rough contact interface are studied. The contact vibration andenergy dissipation characteristics at these interfaces and the transmission performance atmultiple interfaces are presented. The accuracy of the established critical models andthe results are validated through experiments. The main works done in this paper are asfollows:
①The model of an elastic sphere in contact with a rigid flat surface is establishedon the static equilibrium position considering the effect of gravity. The Hertziansphere-plane contact model exhibited liner viscous damping is difficult to accuratelydescribe the contact force-displacement relationship due to the interface properties,damping capacity and other effects. The effect of nonlinear damping on the freevibration responses are studied by employing a general viscous damping functionrelated to the displacement raised to an arbitrary rational positive power law. It is shownthat the feature response parameters are almost identical for different damping modelsand it is thus difficult to identify the damping model. A damping model identification method is therefore proposed based on the restoring force and is validated usingexperimental results. The damping models for spheres with different materials as steeland Low Density Polyethylene (LDPE) are obtained.
②The “single metal block-rigid plane” rough interface model and the “multiplerough surface metal blocks-rigid plane” multiple interfaces model are established tostudy the plastic deformation and energy dissipation for contact interaction normal tothe rough interface. The fractal geometry of rough surface, the continuity hardeningcriterion for plastic material and the amount of plastic energy dissipation equaling to thearea of the loading and unloading curves are coupled to avoid the discontinuity of theelastic-plastic transition. Effects of surface topography, plastic hardening behavior ofmaterial and interface friction on the force-deformation relationship are presented. Theenergy dissipation characteristics due to plasticity hardening and the energy dissipationratio at different interfaces are studied. The plastic contact deformation and the energydissipation meachnism are presented.
③The dynamic model for an elastic block with rough surface in contact with arigid flat surface is established. The rough surface is characterized by self-affine andscale-indenpent fractal geometry and the force-deformation relationship for roughsurface with different topographies are calculated to overcome the scale-denpent defectof current models based on statistical rough surface description. The contact stiffnessexpressions for the rough elastic body and the asperities are further established. Effectof surface topography on the contact stiffness is presented. The natural frequency andthe free vibration energy dissipation for rough solid with different surface topographiesare evaluated. The experimental results on energy dissipation observed for verticalcontact vibration are supported.
④The force-displacement expressions at the connecting end of the slip interfaceare derived for different interface slipping states, including no slip, micro-slip andmacro-slip and the dynamic model for the slipping interface system are furtherestablished. The current models are on the assumption of uniform pressure distributionalong the interface and limit to only studying the effect of micro-slip on the systemvibratiory responses. The established model considered the ununiform pressuredistribution along the interface, and the natural frequency, the amplitude responsesunder harmonic excitation and the energy dissipation per cycle are further calculated fordifferent interface slipping states. The dynamic responses and energy dissipationcharacteristics of the slipping interface system are presented.
⑤The single slipping interface model is extended and the multiple transmittinginterfaces model “Sphere-Joint Assembled Multi-layered Plates”(SJAMP) isestablished to consider the coupling between the frictional interfacial motion alonginterfaces and the normal contact motion. The dynamic responses at the multipleinterfaces under shock excitation are calculated. Expression relates the accelerationamplitude at different interfaces and the shock amplitude is established. Thetransmission of vibration and energy through the multiple interfaces are characterizedby the defined vibration transmission ratio and energy transmission ratio. The inputenergy transmission ratio of the impact energy at the input interface is studied and thevibration and energy transmission characteristics at the multiple interfaces of layeredand jointed plates associated with friction are presented. Experimental validation isperformed and shows good agreement with numerical results.
由于机械接触界面的复杂性和多样性，目前，一些重要的现象和机理尚未解明，尤其是界面的接触刚度和界面阻尼特性、复杂界面特性的界面模型表征、界面的非线性动力学过程、多界面的接触振动现象及其对系统的影响等核心问题一直未得到很好解决。目前，机械界面行为已经成为机械领域中的关键共性的基础科学问题。因此，开展界面接触动力学行为的探索性研究，具有重要的理论意义和实际工程价值。
本论文重点围绕几类基础的接触界面，包括考虑重力作用的球面接触界面、粗糙接触界面、滑移接触界面和层叠多传递界面，通过建立界面接触的动力学模型，研究两类典型界面的接触刚度和阻尼特性，揭示三种典型界面的接触振动与能量耗散特性，以及激励载荷在层叠多界面的振动与能量传递行为，并通过相关实验验证关键模型和计算结果的有效性和准确性。论文的主要工作有以下几个方面：
①针对目前基于Hertz球-刚性平面接触模型，因受接触界面属性、阻尼属性及其他因素的影响，线性粘性阻尼模型难以真实描述界面接触力-变形关系的问题，在考虑真实系统的重力影响因素的基础上，采用任意正指数的非线性粘性阻尼函数，建立了基于静平衡位置的球体-刚性平面接触振动模型，分析了不同的界面非线性阻尼对系统自由振动响应的影响；同时，针对系统响应特征基本相同，通过响应值辨识接触阻尼模型困难的问题，基于接触阻尼回复力-速度关系，提出了一种基于回复力的接触阻尼模型辨识方法，且通过实验方法验证了其有效性，并获得了多种材料属性的球-平面模型的阻尼模型。
②建立了“单层金属板-刚性平面”粗糙界面模型和“多层粗糙金属板-刚性平面”多界面模型，耦合了粗糙表面的分形模型、塑性材料的连续性硬化准则和加载与卸载力-变形曲线形成迟滞环面积等于塑性变形能量耗散量的关系，可较好地解决弹性和塑形的转变过程存在不连续的问题。同时，研究了界面形貌、材料塑性变形行为和界面摩擦对粗糙界面的接触力-变形关系的影响，计算了由塑性变形及硬化引起的能量耗散和多层粗糙界面的能量传递耗散率，揭示了粗糙界面塑性接触变形机理和能量耗散规律。
③采用具有自相似和尺度独立的粗糙表面分形模型，通过计算不同界面形貌接触模型的力-变形关系，构造了粗糙接触界面和表面粗糙体的刚度表达式，建立了基于静平衡位置的弹性粗糙体-刚性平面的粗糙界面接触振动模型，可克服目前粗糙界面的接触刚度、动力学行为和能量耗散基于粗糙表面的统计学模型描述而具有尺度依赖性的缺点。同时，研究了界面形貌对法向接触刚度的影响，计算了不同形貌界面接触振动系统的固有频率和振动能量耗散率，分析了粗糙界面法向接触振动的响应特征与能量耗散特性，并对界面法向微动能量耗散的实验结果进行了解释。
④推导了无滑动、微滑动和整体滑动的不同界面运动状态时滑动界面端部的力-位移关系表达式，建立了滑动界面系统沿滑动方向的动力学模型，解决了目前的滑动界面系统模型局限于界面具有均匀压力分布的假设条件，且仅考虑界面微滑动对系统振动响应特性影响的问题，并在考虑真实界面的非均匀压力分布的基础上，计算了不同滑动界面运动状态滑动界面系统的固有频率、简谐载荷作用下的响应幅值以及每周期的能量损耗量，研究了动态载荷作用下滑动界面系统的动力学响应与能量耗散特性。
⑤考虑实际传递界面法向和切向运动耦合，扩展单一滑动界面模型，建立了“球-螺栓固结多层叠加板”的叠加多传递界面模型（SJAMP），计算了不同冲击激励下多层叠加金属板多传递界面的加速度响应，构造了振动加速度幅值与冲击激励的关系表达式，引入振动传递率与能量传递率的概念并计算了各传递界面的振动与能量传递率，分析了输入界面对冲击能量的传递率与冲击能量的关系，以及冲击激励沿非连续多界面传递时的振动与能量传递特性，并通过实验测试验证了计算结果的可靠性。
The vibration characteristics and energy dissipation mechanism at contactinterfaces not only significantly affect the dynamic performance of mechanical system,but also greatly affect the amplitude, frequency and phase responses of measuredcharacteristic signal, and thus further influence the accuracy and reliability of machinerycondition mointering. Due to the complexity and diversity of contact interfacesassociated with mechanical system, the mechanism of some very importantphenomenons are unclear, especially the critical problems as stiffness and dampingcharacteristics at contact interfaces, model characterization for interface with complexattribution, nonlinear dynamic process, contact vibration at multiple interfaces and itseffect on system. The interface properties have become the basic key problem inmechanical area. Therefore, it is of great significance to explore the contact dynamics atinterfaces.
This thesis foucuses on the nonlinear vibration characteristics and energydissipation mechanism of several basic contact interfaces, including sphere contactinterface considered the effect of gravity, rough contact interface, sliding contactinterface and layered multiple transmitting interfaces. The dynamic models areestablished and the contact stiffness and damping characteristics of two type interfaces,i.e., the sphere and the rough contact interface are studied. The contact vibration andenergy dissipation characteristics at these interfaces and the transmission performance atmultiple interfaces are presented. The accuracy of the established critical models andthe results are validated through experiments. The main works done in this paper are asfollows:
①The model of an elastic sphere in contact with a rigid flat surface is establishedon the static equilibrium position considering the effect of gravity. The Hertziansphere-plane contact model exhibited liner viscous damping is difficult to accuratelydescribe the contact force-displacement relationship due to the interface properties,damping capacity and other effects. The effect of nonlinear damping on the freevibration responses are studied by employing a general viscous damping functionrelated to the displacement raised to an arbitrary rational positive power law. It is shownthat the feature response parameters are almost identical for different damping modelsand it is thus difficult to identify the damping model. A damping model identification method is therefore proposed based on the restoring force and is validated usingexperimental results. The damping models for spheres with different materials as steeland Low Density Polyethylene (LDPE) are obtained.
②The “single metal block-rigid plane” rough interface model and the “multiplerough surface metal blocks-rigid plane” multiple interfaces model are established tostudy the plastic deformation and energy dissipation for contact interaction normal tothe rough interface. The fractal geometry of rough surface, the continuity hardeningcriterion for plastic material and the amount of plastic energy dissipation equaling to thearea of the loading and unloading curves are coupled to avoid the discontinuity of theelastic-plastic transition. Effects of surface topography, plastic hardening behavior ofmaterial and interface friction on the force-deformation relationship are presented. Theenergy dissipation characteristics due to plasticity hardening and the energy dissipationratio at different interfaces are studied. The plastic contact deformation and the energydissipation meachnism are presented.
③The dynamic model for an elastic block with rough surface in contact with arigid flat surface is established. The rough surface is characterized by self-affine andscale-indenpent fractal geometry and the force-deformation relationship for roughsurface with different topographies are calculated to overcome the scale-denpent defectof current models based on statistical rough surface description. The contact stiffnessexpressions for the rough elastic body and the asperities are further established. Effectof surface topography on the contact stiffness is presented. The natural frequency andthe free vibration energy dissipation for rough solid with different surface topographiesare evaluated. The experimental results on energy dissipation observed for verticalcontact vibration are supported.
④The force-displacement expressions at the connecting end of the slip interfaceare derived for different interface slipping states, including no slip, micro-slip andmacro-slip and the dynamic model for the slipping interface system are furtherestablished. The current models are on the assumption of uniform pressure distributionalong the interface and limit to only studying the effect of micro-slip on the systemvibratiory responses. The established model considered the ununiform pressuredistribution along the interface, and the natural frequency, the amplitude responsesunder harmonic excitation and the energy dissipation per cycle are further calculated fordifferent interface slipping states. The dynamic responses and energy dissipationcharacteristics of the slipping interface system are presented.
⑤The single slipping interface model is extended and the multiple transmittinginterfaces model “Sphere-Joint Assembled Multi-layered Plates”(SJAMP) isestablished to consider the coupling between the frictional interfacial motion alonginterfaces and the normal contact motion. The dynamic responses at the multipleinterfaces under shock excitation are calculated. Expression relates the accelerationamplitude at different interfaces and the shock amplitude is established. Thetransmission of vibration and energy through the multiple interfaces are characterizedby the defined vibration transmission ratio and energy transmission ratio. The inputenergy transmission ratio of the impact energy at the input interface is studied and thevibration and energy transmission characteristics at the multiple interfaces of layeredand jointed plates associated with friction are presented. Experimental validation isperformed and shows good agreement with numerical results.
引文
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