New insights into folding tape-spring

The tape-spring is widely used in aerospace, mechanical, and civil engineering due to its unique mechanical properties and compact size. This paper aims to establish a new analytical model to more accurately predict the folding behavior of the tape-spring, including the geometric configuration, folding moment versus longitudinal curvature curve, peak moment, and propagation moment. This model comprehensively considers the influence of stretching strain energy and bending strain energy on the total strain energy, and determines the folding behavior of the tape-spring through the minimum energy principle. The proposed analytical model was compared with Wuest's model, Yee's model, and Yao's model. Experiments of tape-springs made from two different materials were utilized for validation. The study shows that the proposed model has the highest prediction accuracy compared with the classical models, with the error of approximately 10%. The reason for the significant difference in the prediction results between the proposed model and Yao's model was given, and the relationship between stretching strain energy and bending strain energy during the folding process of the tapespring was analyzed. The proposed model has broader applicability than classical models and provides new insights and solutions for accurate prediction of the folding behavior of the tape-spring.