中文摘要：

机械系统因热膨胀和热弯曲引起的热误差是工程研究的一个重要问题。为了研究热效应对柔性多体系统动力学特性的影响，本文首先从虚功原理出发，用假设模态法对平面梁进行离散，在温度变化和y方向的温度梯度已知的情况下，建立了单个柔性梁的动力学变分方程，然后根据各柔性体之间的运动学约束关系，引入拉格朗日乘子，建立了柔性多体系统的第一类拉格朗日动力学方程，并推导了约束力的计算公式。曲柄滑块机构的数值仿真表明：温度变化对系统动力学特性的影响不仅与温度变化率和系统惯量有关，还取决于几何位置。当运动机构趋近于奇异位置时，热效应最为显著。进一步研究表明，温度梯度引起横向变形和横向约束力平均值的变化。

英文摘要：

Thermal error of a mechanism due to thermal expansion and thermal bending is an important problem in engineering. In order to investigate the thermal effect on the dynamic performance of a flexible multibody system, dynamic equations of a flexible beam are established based on virtual work principle, and then assumed mode method is employed for discretization. Based on the assumption that the temperature change and the temperature gradient in y direction are known, the generalized mass and force matrices for a single beam are derived. According to the constraint equations between flexible beams, the Lagrange＇s dynamic equations for the first kind are established and the constraint force expressions are obtained. Simulation of a crank-slider system shows that the thermal effect due to temperature variation is related to geometric position as well as temperature increasing rates and geometric proper- ties. Significant thermal effect is shown when the mechanism approaches singular configurations. Furthermore, it is indicated that temperature gradient induces transverse deformation and leads to the change in the average value of the transverse constraint force.