Computational nonlinear thermoelastic deformation and undamped natural frequency analysis of a tensile nylon V-actuator

Abstract

This article investigates the effects of geometric nonlinearity and thermal loading on the thermal stroke and natural vibration of a tensile nylon actuator. The proposed single-degree-of-freedom configuration consists of two identical tensile nylon springs arranged in a V-shape (V-actuator). Loaded by an attached gravitational mass at its actuation point and subjected to thermal loading, the actuator exhibits both negative thermal expansion and compressive prestress. The thermomechanical actuating force induced by the thermal shortening of the actuator springs lifts the attached external mass. This setup demonstrates a significant increase in both the thermal stroke and tensile action force compared to a parallel spring arrangement under an identical gravitational load. The natural frequency of the actuator’s undamped small vibrations is determined from the static deflection induced by the external gravitational mass and the thermal state of the springs. A computational model is developed based on the measured tensile characteristics of the individual springs and the complete V-actuator assembly. Utilising the updated Lagrangian formulation (ULF) for large displacements and a custom nylon twisted coiled spring (NTCS) finite element, nonlinear incremental equations are established to calculate the elastic extension, thermoelastic shortening, and total static deflection of the actuator’s operating point. These equations are solved using the incremental Newton method. The results of this nonlinear algorithm are compared with a classical linear spring model and selected numerical simulations are validated through experimental measurements on a physical prototype. The findings reveal that geometric nonlinearity and heating significantly influence the actuator’s thermal stroke and the natural frequency of the oscillating attached mass.