零热膨胀系数三角形结构的理论与实验研究

Theoretical and Experimental Study on the Triangular Structure With Zero Thermal Expansion Coefficient

分别对铰接和固结节点的基于不同材料的三角形单元高度方向热膨胀系数进行了理论推导,给出了其为零的条件及设计公式。研究表明,两种三角形单元在结构尺寸一致的条件下,高度方向热膨胀系数接近相同,即与节点型式接近无关。设计了实验装置,采用分辨率为5nm的位移传感器和分辨率为0.02℃的铂温度传感器,在实验室内对铰接节点的基于普通铝材和钢材的三角形单元高度方向进行了热膨胀系数实测,测量结果为,在20～40℃温度区间内,其热膨胀系数达1.59×10^(-6)±0.23/℃,约为普通碳钢材料热膨胀系数的1/7。验证了利用两种具有不同热膨胀系数的普通材料通过合理设计,有望实现较低的热膨胀系数,从而可能替代昂贵的专用贵重材料来制造精密机械的支撑和定位机构,用以消除温度变化引起的热胀冷缩对系统性能的影响,尤其适用于基于三角形单元结构的天文望远镜桁架镜筒的设计。

Therotical research was first carried out for the calculation of theimal expansion coefficient （TEC） a-long height direction for two basic triangular structures based on both pinned and welded node types, respectively. The conditions for realizing zero TEC were then figured out, which may guide realistic design of triangle-based structure. Further research confirms that the both triangles exhibit nearly the same TEC when they are design with the same mate- rials and dimensions, to be general, the TEC is almost independent of the node type. Afterwards, a test setup was es- tablished to measure the TEC of a pin-node triangular truss designed with common industrial materials aluminum and steel. Displacement sensor and platinum temperature sensor with output resolutions of 5 nm and 0.02℃, respectively, are used throughout the test, The results indicate that the measured TEC, between 20-40℃, is 1.59×10^-6±0. 23/℃, which is about 1/7 that of common steel. The work presents possibility of building low thermal expansion sup- porting and positioning structure with common cheaper materials with different TECs, as provides an optional substitu- tion to the expensive materials normally used, thanks to their low TEC, for precision machine and instruments to elimi- nate thermal disturbance. Particularly, the basic triangular structure with zero TEC concept fits well the tube truss de-sign for astronomical telescopes.