Compliance modeling and strain analysis of double-hole force sensor

Double-hole force sensors are widely used in aerospace, industrial metrology and other fields, but their load-displacement characteristics and strain-load relationship are difficult to be formulated analytically due to the variable cross-section design, which will affect the design and performance optimization of multi-axis force sensors with double-hole structure. This study uses the compliance matrix modeling method to build the overall compliance model of the double-hole force sensor after determining the compliance matrix and strain-load relationship of the force-sensitive element with variable cross-section based on the elastic-beam theory. The analytical relationship between the sensed strain of the strain gauges on the force-sensitive element of the double-hole structure and the applied load acting on the force-measuring end of the sensor is finally obtained with the compliance model. The presented model and strain analytical relationship are validated by the finite element analysis and experiment, respectively. The results show that the relative errors for the expected-dimensional analytical compliances relative to finite element results are within 3%, and the bridge output voltages are within 5% compared with experimental results. These findings demonstrate that the analytical equations that were derived are capable of accurately assessing the load-displacement characteristics of double-hole force sensors as well as the mapping between applied loads and bridge output strains. They can also offer dependable technical assistance for the best possible design of multi-axis force sensors that have double-hole structures.