Dynamic characteristics of the sliding guide in a telescopic mechanism

The sliding guide used in the telescopic mechanisms of morphing aircraft typically exhibits large clearance and low stiffness, resulting in complex dynamic behavior that significantly affects mechanism performance. Most existing studies on sliding guide dynamics focus on machine tool guides, which differ substantially in structural and operating conditions. Therefore, a specialized dynamic model that accounts for guide flexibility and clearance effects is needed to accurately characterize the dynamic performance of telescopic sliding guides.

A dynamic model of a sliding guide with clearance was developed. The guide rail was represented by finite element beam elements based on the Euler–Bernoulli beam theory to capture its elastic deformation. A multipoint contact detection method was introduced to avoid missed detections of contact states between the slider and the deformed guide. Contact may occur in either line or area contact modes. To compute the contact force in area contact mode, a variable stiffness contact force model was proposed; its damping coefficient was chosen manually. Because different contact mode calculations could produce large discrepancies in contact force and cause numerical instability, a modified variable stiffness contact force model was introduced for area contact, in which the damping coefficient was corrected using the material restitution coefficient. For line contact, the Flores contact force model was adopted. Friction forces were calculated using the Ambrósio modified Coulomb friction model. The dynamic equations of the slider and the guide were formulated using the Lagrange multiplier method with Baumgarte stabilization. A unified numerical solution strategy based on MATLAB's ode15s solver was implemented to simulate the dynamic response.

Numerical simulations revealed the influence of key parameters on dynamic behavior. When guide elasticity was included, peak contact forces decreased, but the lateral displacement of the slider increased, accompanied by sustained oscillation owing to cantilevered guide vibration. Larger clearance sizes yielded higher peak contact forces and larger amplitude oscillations in guide tip deflection, while the time-averaged friction force decreased. In a dual-stage, dual-guide configuration, the system exhibited more frequent collisions and chaotic lateral motion, with notable jamming caused by asynchronous deformation of the two guides. Reducing the interguide spacing mitigated this jamming effect. Experimental validation using a prototype with adjustable clearance showed that the equivalent friction coefficient decreased with increasing clearance under different actuation speeds and modes, consistent with simulation trends. This effect was more pronounced during deployment than during retraction and at lower speeds. The effect diminished at larger clearances, exhibiting nonlinear saturation. The deviation between simulated and experimental friction coefficients was within 30.00%, confirming the validity of the proposed dynamic model.

This paper presents a comprehensive dynamic modeling framework for sliding guides in telescopic mechanisms that incorporates guide elasticity and clearance effects. The proposed contact detection method and modified contact force model increase modeling accuracy and numerical stability. The simulation and experimental results demonstrate that guide elasticity, clearance size, and guide configuration considerably affect dynamic behavior. These findings provide a theoretical foundation for the design and control of sliding guides in deployable aerospace mechanisms.