# Thermo-Mechanical Coupled Analysis of Electric Vehicle Drive Shafts
## 2 Finite Element Method for CV Joint  
In this study, the primary focus is on analyzing the CV joint, a critical component of the drive shaft in electric vehicles. The CV joint consists of multiple interconnected parts, resulting in a highly complex geometry and intricate operational mechanisms. The model used in this study, as illustrated in Figure 1, incorporates a novel joint design named the ball spline joint (BSJ), which combines a high-efficiency constant velocity (CV) joint with a ball spline structure capable of accommodating various angular movements [21]. To simulate the heat generated during the operation of this component, the analysis was conducted under the assumption that it rotates continuously at a fixed angle. The ball spline joint (BSJ) is designed to transmit power smoothly across a range of angles, from 0 degrees (straight-line driving) to 40 degrees (high-angle operation). Its design incorporates a ball spline structure in the center, allowing for seamless power transmission while accommodating suspension movements. However, for the purposes of this study, the ball spline movement was assumed to remain stationary to simplify the analysis. The BSJ comprises a power transmission joint section, consisting of an outer race, inner race, cage, and ball, as well as a ball spline shaft and a sleeve cage with balls. This integrated structure connects with the inner race of the CV joint, enabling the axial movement of the drive shaft and accommodating changes in vehicle ground clearance through the ball spline coupling mechanism. The BSJ transmits the rotational torque generated by the motor, during which the internal components undergo high-speed rotation. This operation induces friction among the internal components, leading to heat generation. Such thermal phenomena can cause a thermal deformation or expansion of the internal parts, resulting in the accumulation of internal stress. However, due to the geometric characteristics of the BSJ, directly observing the phenomena occurring within the joint during operation poses a significant challenge. In particular, the real-time observation or experimental validation of factors such as stress distribution changes, stress concentration, deformation, heat genera tion, and thermal stress during operation is highly constrained. Furthermore, as the BSJ is characterized by high-speed rotation and prolonged operation, performing long-term simulations of its real-world performance is inherently challenging. In prior studies, quasi-static analysis has been employed to evaluate the contact forces and plastic deformation of constant velocity (CV) joint components for passenger vehicles [22]. However, quasi-static analysis is limited in its ability to account for time-dependent phenomena, as it evaluates systems under static conditions. This approach fails to adequately describe dynamic phenomena such as friction and plastic deformation arising from contact structures. To address these limitations, this study employs a combined approach using both Explicit and Implicit analysis methods to comprehensively simulate not only structural deformations during dynamic operation but also thermal interactions. The analyses were conducted using the Transient Thermal module of LS-Dyna and Ansys Mechanical. LS-Dyna is a software specialized in nonlinear finite element analysis, offering significant advantages in analyzing rapidly changing dynamic conditions through its Explicit analysis method [23; 24; 25; 26]. Explicit analysis is particularly suited for physical phenomena that occur over short time spans, such as impacts, explosions, and collisions. It provides robust solutions for simulations involving nonlinearities and complex contact conditions, ensuring high stability even under challenging scenarios. Moreover, Explicit analysis excels in efficiently solving problems involving large deformations or multiple contact points, significantly reducing computation time while delivering reliable results.