Multibody dynamics modeling and simulation of high-speed flexible sled-track systems

The high-speed sled-track system is a critical ground test device for evaluating the performance of aircraft and other equipment under extreme speed conditions. The sled accelerates along the track, constrained by slippers. The clearance between the slippers and tracks typically induces nonlinear behaviors such as collision, friction, and wear. These behaviors can lead to bifurcation, chaos, and violent vibrations in the system, as well as the propagation and complex superposition of elastic waves in the tracks. The sled system exhibits time-varying characteristics due to the continuous consumption of propellant. In particular, under various excitations such as track irregularities, nonlinear aerodynamic loads, and engine thrust oscillations, the sled dynamically couples with the track. To address the coupled dynamic problem of this time-varying and nonlinear system under multiple excitations, the sled and track were treated as flexible bodies that could deform under applied forces, and a multibody dynamics modeling and simulation of the high-speed flexible sled-track system was conducted. This study enhances the understanding of nonlinear dynamic issues caused by slipper-track clearance and reveals the interaction between the sled and track, thereby providing guidance for the dynamic design and optimization of the sled-track system. 1. The multibody dynamics modeling of the slipper-track system forms the foundation for the multibody dynamics modeling of the sled-track system. A multibody dynamics model of the rigid slipper-track system with clearance was developed. To address the nonlinear issues associated with slipper-track clearance, the system underwent bifurcation analysis and chaos identification, and various nonlinear behaviors, such as the super-harmonic responses of the slipper, were predicted. The results indicated that as bifurcation parameters, such as the slipper’s length, changed, the slipper’s motion transitioned between periodic, quasiperiodic, and chaotic states. Correspondingly, the type of attractor varied between fixed points, limit cycles, and strange attractors. By examining these bifurcations, the reasons for inconsistencies in current studies regarding the influence of slipper-track clearance on the slipper’s dynamic responses were clarified, providing a foundation for the dynamic design of the slipper and track. 2. To address the challenge of simulating the interaction between the elastic effect of a long track and the dynamic responses of the slipper, a rigid-flexible coupling multibody modeling method based on virtual sliding nodes was proposed. The flexible track dynamic model, constructed using finite volume discretization, successfully avoided the shear locking issue commonly encountered with traditional finite element discretization methods. The accuracy of this flexible track model was verified through modal testing of the track. In the rigid-flexible coupling multibody dynamics simulation of the slipper-track system, given the low computational efficiency of modeling long flexible tracks and the problem of elastic wave reflection at the window end in traditional sliding window methods, an efficient simulation approach, termed the transfer window method, was proposed to suppress elastic wave reflection. Numerical examples demonstrated that the proposed modeling and simulation method effectively facilitated the efficient simulation of interactions between the rigid slipper and the long flexible track. 3. To address the challenge of predicting the dynamic responses throughout the entire process of a sled accelerating to its maximum velocity along the track, a multibody dynamics modeling and simulation method for the flexible sled-track system was proposed. This method accounted for various excitations, time-varying characteristics, and nonlinearities, enabling the rapid prediction of the dynamic responses of the flexible sled as it travels along multi-kilometer flexible tracks to high speeds. The effectiveness of this simulation method and the importance of considering the flexibility of the sled-track system for precise dynamic response predictions were validated through sled tests. Simulation results indicated that the main frequencies of the sled cabin’s dynamic responses corresponded to the system’s time-varying natural frequencies throughout the entire process. The acceleration of the slipper exhibited super-harmonic responses, with each main frequency being an odd multiple of the fundamental frequency. Regarding the elastic waves in the track, the larger wavelength corresponded to the distance traveled by the slipper between two contacts with the track, while the smaller wavelength matched the distance between adjacent track support blocks. 4. To address the challenge of simulating the interaction between the dynamic responses of extremely high-speed flexible sled-track systems and the wear characteristics of slippers, a co-simulation method for the multibody dynamics of flexible sled-track systems and slipper wear prediction was proposed. The dynamic responses of the flexible sled traveling along the long flexible track were predicted, and the wear thickness of each slipper was computed throughout the entire acceleration process. Simulation results indicated that the cumulative wear thickness of the left and right contact surfaces of the slipper increased alternately in a step-by-step manner over time, while the lateral and vertical cumulative wear thickness of each slipper generally increased exponentially with time. The wear clearance had varying effects on the acceleration of different slippers, with the fundamental cause being the bifurcation of the nonlinear system due to slipper-track clearance.

Il sistema slitta-rotaia ad alta velocità costituisce un dispositivo sperimentale fondamentale per la valutazione delle prestazioni aeronautiche e di altri equipaggiamenti in condizioni estreme di velocità. La slitta, accelerata lungo la rotaia mediante pattini di guida, manifesta comportamenti non lineari indotti dal gioco tra pattini e rotaia, tra cui collisioni, attrito e usura. Tali fenomeni possono condurre a biforcazioni, dinamiche caotiche, vibrazioni violente, nonché alla propagazione e sovrapposizione complessa di onde elastiche nella struttura della rotaia. Il sistema presenta caratteristiche tempo-varianti dovute al consumo progressivo del propellente. L'interazione dinamica tra slitta e rotaia risulta ulteriormente complicata da eccentricità del binario, carichi aerodinamici non lineari e oscillazioni di spinta del motore. Per affrontare queste problematiche di accoppiamento dinamico in condizioni multi-eccitazione, è stato sviluppato un modello multivariabile che considera entrambi i componenti come corpi deformabili, implementando una metodologia innovativa di simulazione dinamica. 1. La modellazione dinamica del sistema pattino-rotaia con gioco meccanico costituisce la base per l'analisi del sistema completo. Attraverso analisi di biforcazione e identificazione di caos, sono stati caratterizzati comportamenti non lineari quali risposte super-armoniche del pattino. I risultati dimostrano che parametri di biforcazione come la lunghezza del pattino inducono transizioni tra stati periodici, quasiperiodici e caotici, con corrispondente variazione degli attrattori da punti fissi a cicli limite e attrattori strani. Questa analisi chiarisce le discrepanze negli studi esistenti sull'influenza del gioco meccanico, fornendo basi teoriche per la progettazione dinamica ottimizzata. 2. Per simulare l'interazione tra effetti elastici della rotaia lunga e risposte dinamiche del pattino, è stato proposto un metodo innovativo basato su nodi virtuali di scorrimento. La discretizzazione a volumi finiti della rotaia flessibile evita il problema di blocco a taglio tipico degli elementi finiti tradizionali. La validazione modale conferma l'accuratezza del modello. Per superare le limitazioni computazionali e i fenomeni di riflessione d'onda nei metodi a finestra mobile, è stato implementato un approccio "transfer window" che inibisce efficacemente la riflessione delle onde elastiche. Applicazioni numeriche dimostrano l'efficienza del metodo proposto. 3. Un metodo integrato di modellazione multivariabile consente la previsione delle risposte dinamiche durante l'intera fase di accelerazione della slitta lungo binari flessibili plurichilometrici. I test sperimentali validano l'importanza di considerare la flessibilità del sistema per previsioni accurate. L'analisi rivela che le frequenze dominanti delle risposte dinamiche della cabina corrispondono alle frequenze naturali tempo-varianti del sistema. Le accelerazioni dei pattini presentano risposte super-armoniche con rapporti di frequenza interi dispari. Le lunghezze d'onda delle onde elastiche nella rotaia correlano sia con la distanza tra contatti successivi dei pattini che con l'intervallo tra supporti strutturali. 4. Un metodo cosimulativo combina dinamica multivariabile e previsione d'usura dei pattini. I risultati dimostrano un incremento graduale a gradini dello spessore d'usura cumulativo sulle superfici laterali, contrapposto a un aumento esponenziale nelle direzioni verticale e trasversale. L'analisi rivela che il gioco da usura influenza differenzialmente l'accelerazione dei vari pattini, con meccanismi riconducibili a fenomeni di biforcazione del sistema non lineare. Questa metodologia fornisce strumenti predittivi fondamentali per l'ottimizzazione della durata operativa del sistema.