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毕业设计说明书（论文）中文摘要本文旨在保留系统的刚性假设的前提下，研究非理想情况下刚体相对滑动时的自锁现象。本文同时考虑了杆的整体弯曲柔度和轴向拉压柔度，提出了含弹簧阻尼系统的多段杆离散模型来模拟杆的柔度，并在此框架内研究了奇异性的难点问题，以期实现对非光滑接触刚体系统的理论探索。本论文通过线性互补方法（LCP），建立了含非理想单边约束的刚体接触问题的动力学模型。杆的运动过程分为三种：滑动、粘滞和飞离。其中滑动可以转变为粘滞或者飞离，因此我们主要研究了滑动模式下系统的状态，并且得到发生其它两种情形的条件。通过相关函数进行了近似化简，并利用 origin 软件，得到直观的图形表达，得到了在不同整体柔度情况下，系统奇异点的位置以及各种模式的发生区间情况。研究结果证明影响奇异情况发生的主要原因是摩擦系数，而与我们所取的杆的整体柔度关系很小。6645
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关键字 单边约束 自锁 奇异性
毕业设计说明书（论文）外文摘要
Title New theoretical solutions for the self-locking problem of a rigid
body relative sliding on rough ground
Abstract
The aim of the paper is, based on the foundation of the reservation of system rigidity
assumption, to conduct researches on the self-locking of rigid body under the non-ideal
condition of relative sliding. Besides, considering the whole rigidity of the rod, this
paper proposed a method, which is using discrete model of multi-section rod containing
spring-damp system to simulate the flexibility of the rod. After the previous work, the
paper explored the difficult problem of singularity, in order to complete the theoritical
discovery of the non-smooth contacted rigid body system. By using the method of the
linear complementary problem(LCP), this paper established a dynamic model involing
the rigid body contact problem under the condit ion of non-ideal unilateral constraints.
The movement process of the rod can be devide into three types: sliding phase, stick
phase and flight phase. Because the sliding phase can be converted to stick phase or
flight phase, this paper mainly researched the status of the system under the sliding
mode and the preconditions to trigger the occurrence of the other two phases. By the
approximate simplifying of the correlation function, we got the direct expression of
diagram. Also, under the perse conditions of whole flexibility of the rod, we used the
ORIGIN analysis software to obtain the location of the system singularity as well as the
occurred region of different modes. The result proved that, instead of the whole
flexibility of the rod we picked, the major reason leading to the occurrence of the
singularity is coefficient of friction of rough surface.
Keywords unilateral constraints self-locking singularity
目 次
1绪论 1
1.1问题背景分析 1
1.1.1碰撞、接触问题的背景分析 1
1.1.2互补性问题的数学背景 3
1.1.3单边约束系统动力学的研究背景 4
1.2本文的主要工作和创新点 . 6
2经典PAINLEVÉ问题 7
2.1 PAINLEVÉ问题的光滑动力学解 . 7
2.2自锁弹跳的原因和粘滑运动 . 9
3 实验观察 11
4考虑弯曲柔度的多段模型 . 12
4.1模型建立 12
4.2模型简化 13
4.3动力学方程 13
4.4系统的四种模式 14
4.5 MⅡ模式的研究 . 15
结论 . 23
致谢 . 24
参考文献 . 25