Efficient Simulation of Multi-Body Dynamics with Roller Guide Joints Using Julia

Due to the existence of nonlinearities in mechanical systems, considerable concern has arisen regarding the effectiveness of solving multi-body dynamics (MBD) problems. Although simulations of traditional mechanisms with perfect joints could be solved with high efficiency, joints in practical applications are often characterized by clearances, leading to a significant reduction in simulation efficiency for such cases. Enhancing the effectiveness of solvers is essential for simulating systems with nonlinearities. This paper presents an exploration of using Julia, a high-performance, open-source programming language, to solve MBD problems based on index-1 differential-algebraic equations (DAE). Quaternions were utilized to represent the orientation of the rigid bodies. Alongside the modelling of common perfect joints, both planar perfect and imperfect roller guide joints were included to illustrate the method's adaptability in addressing non-standard joint types. Two case studies were provided to evaluate the implementation: the first involved a classic crank-slider mechanism, where a roller-guide joint replaced the traditional translational joint; the second examined a vehicle sliding door system. The results were also validated through experiments conducted on the sliding door mechanism. Results from the Julia implementation were compared with those from a MATLAB implementation to assess computational performance under identical conditions. The study emphasized efficiency, particularly regarding the simulation of clearance joints. Furthermore, an investigation was conducted into the performance of modern differential equation solvers available in Julia to evaluate their efficiency and accuracy in solving MBD problems. The findings suggest that Julia offers certain advantages in computational performance, particularly in dealing with systems involving nonlinearities.