Tripod constant velocity (TCV) joints are common components in automotive and mechanical applications. The benefits of the TCV joint are its high plunge capacity and high torque capacity. During power transmission, the friction inside the joint generates an axial force according to the kinematics. This force causes noise and vibration problems. In this study, a simplified multi-body dynamic model based on a phenomenological TCV joint friction model is developed. This model considers the generated axial force (GAF) of a TCV joint with different lubricate conditions. The efficiency and accuracy are verified by comparison with other prediction models and experiments. Thus, this model can be used to design and control the manufacture process of TCV joints.