柱式弹性体的端面载荷分布和结构尺寸对端部效应的影响规律

端部效应是影响柱式弹性体桥路输出的重要因素之一。本文以长径比为1.0的柱式弹性体为研究对象并基于弹性力学理论研究其受载条件和尺寸效应对端部效应的影响规律。首先,根据端面受载条件和尺寸效应两种力学模型建立位移函数表示的平衡微分方程;其次,以受载条件的力学模型为例,引入两个位移函数对平衡方程进行解耦,推导出对应的力学模型解析解,并根据边界条件确定解析解的待定系数;最后,依据胡克定律和柱式弹性体桥路输出公式计算端面受载条件和尺寸效应对端部效应的影响。计算结果表明：弹性体非均匀载荷分布的一端,端部效应变化更剧烈;而均匀载荷分布的一端,随着弹性体长径比的增大,端部效应受到端面载荷分布的影响越小。此外,端部效应对小尺寸弹性体十分敏感,但当弹性体尺寸增大超过3.5倍时,通过增大尺寸来抑制端部效应的效果迅速消失。研究结果为柱式负荷传感器的设计提供理论指导依据。

End effect of a cylindrical elastomer under different loading distribution and structure size

The end effect is one of the important factors affecting the output of cylindrical elastomer bridge . In this paper, the cylindrical elastomer with the aspect ratio of 1.0 is taken as the research object and the influence of load conditions and size effect on the end effect is studied based on the theory of elasticity. Firstly, the equilibrium differential equations expressed by displacement function were established according to two mechanical models of load conditions and size effect. Secondly, taking the mechanical model of load conditions as an example, two displacement functions were introduced to decouple the equilibrium equations, and the corresponding analytical solution of the mechanical model was derived, and the undetermined coefficients of the analytical solution were determined according to the boundary conditions. Finally, according to Hooke"s law and the output formula of cylindrical elastomer bridge, the influence of load conditions and size effect on end effect was calculated. The calculation results show that the end effect changes more sharply at one end of the elastic body"s non-uniform load distribution. At one end of uniform load distribution, the end effect is less affected by end load distribution with the increase of aspect ratio of elastomer. In addition, tip effect is very sensitive to small size of elastomer, but when the size of elastomer increases by more than 3.5 times, the effect of restraining tip effect by increasing size disappears rapidly. The research results provide theoretical guidance for the design of column load sensor.