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

Nonlinearities in mechanical systems pose significant challenges for efficiently solving multi-body dynamics (MBD) problems. Although simulations of traditional mechanisms with perfect joints can be performed efficiently, joints in practical applications are often characterized by clearances, leading to reduced simulation efficiency and accuracy. Improving solver effectiveness is essential for simulating systems with nonlinearities. This paper explores the use of Julia, a high-performance open-source programming language, to solve MBD problems formulated as index-1 differential-algebraic equations (DAEs). Euler parameters (quaternions) are employed to represent the orientation of rigid bodies. To illustrate the method's adaptability in addressing non-standard joint types, both perfect and imperfect (with clearance or friction) planar roller guide joints are modeled alongside common perfect joints. A case study of a vehicle sliding door system is presented. The numerical results are validated through experiments conducted on the same sliding door mechanism, demonstrating the model's accuracy in capturing the dynamic behavior of the system. Results from the Julia implementation are compared with those from the MATLAB implementation to assess computational performance under identical conditions. The study emphasizes efficiency improvements, particularly in simulating joints with clearances, where nonlinear contact and friction forces increase the computational costs. The findings indicate that Julia offers advantages in computational efficiency, achieving about a 5% reduction in CPU time compared to MATLAB on average. By demonstrating both the modeling accuracy and computational efficiency, this research highlights the potential of Julia as an effective tool for simulating complex MBD systems with nonlinearities. The methodology can be extended to other mechanical systems with similar joint with clearance or friction, improving the accuracy and efficiency of dynamic analysis in engineering applications.