Highly dynamic machining forces can cause excessive and unstable vibrations when industrial robots are used to perform high-force operations such as milling and drilling. Implementing appropriate optimization and control strategies to suppress vibrations during robotic machining requires accurate models of the robot's vibration response to the machining forces generated at its Tool Centre Point (TCP). The existing models of machining vibrations assume the linearity of the structural dynamics of the robotic arm. This assumption, considering the inherent nonlinearities in the robot's revolute joints, may cause considerable inaccuracies in predicting the extent and stability of vibrations during the process. In this paper, a Single Degree Of Freedom (SDOF) system with nonlinear restoring force is used to model the vibration response of a KUKA machining robot at its TCP (i.e. machining tool-tip). The experimental identification of the restoring force shows that its damping and stiffness components can be approximated using cubic models. Subsequently, the Higher-order Frequency Response Functions (HFRF) of the SDOF system are estimated experimentally, and the parameters of the SDOF system are identified by curve-fitting the resulting HFRFs. The accuracy of the presented SDOF modelling approach in capturing the nonlinearity of the TCP vibration response is verified experimentally.